74:@0.058194:0.966765:0.075166:0.966765:0.075166:0.950778:0.058194:0.950778:0.000000:0.000000
Aplicaciones geométricas en:@0.404235:0.116974:0.747240:0.116974:0.747240:0.072315:0.404235:0.072315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.747240:0.116974:0.755884:0.116974:0.755884:0.072315:0.747240:0.072315:0.000000
:@0.755884:0.114975:0.792170:0.114975:0.792170:0.079896:0.755884:0.079896:0.000000
2:@0.792171:0.100623:0.800844:0.100623:0.800844:0.074587:0.792171:0.074587:0.000000
M.5.2.15. Aplicar el producto escalar entre dos vectores, la norma de un vector, la distancia entre dos puntos, el ángulo entre dos vectores y la proyección ortogonal de un vector :@0.143847:0.942492:0.894420:0.942492:0.894420:0.932450:0.143847:0.932450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sobre otro, para resolver problemas geométricos, reales o hipotéticos en R .:@0.143847:0.951293:0.466466:0.951293:0.466466:0.941251:0.143847:0.941251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.461774:0.947427:0.464789:0.947427:0.464789:0.941572:0.461774:0.941572:0.000000
Producto escalar en :@0.404236:0.136533:0.567387:0.136533:0.567387:0.118850:0.404236:0.118850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.567388:0.134803:0.580693:0.134803:0.580693:0.121941:0.567388:0.121941:0.000000
2:@0.580691:0.129703:0.586399:0.129703:0.586399:0.119394:0.580691:0.119394:0.000000
Definición:@0.404236:0.153703:0.484320:0.153703:0.484320:0.136757:0.404236:0.136757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,       con   = ( ,  ),   = ( ,  ).:@0.484322:0.153240:0.794843:0.153240:0.794843:0.136743:0.484322:0.136743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.529017:0.153356:0.555757:0.153356:0.555757:0.136887:0.529017:0.136887:0.000000:0.000000:0.000000
 :@0.532100:0.151216:0.554948:0.151216:0.554948:0.135398:0.532100:0.135398:0.000000:0.000000:0.000000
:@0.561013:0.152722:0.575666:0.152722:0.575666:0.139349:0.561013:0.139349:0.000000
:@0.579808:0.152154:0.593113:0.152154:0.593113:0.139291:0.579808:0.139291:0.000000
2:@0.593113:0.146887:0.598066:0.146887:0.598066:0.137269:0.593113:0.137269:0.000000
A:@0.633301:0.153356:0.644571:0.153356:0.644571:0.136887:0.633301:0.136887:0.000000
:@0.636383:0.151216:0.642799:0.151216:0.642799:0.135398:0.636383:0.135398:0.000000
a b B:@0.667844:0.153356:0.724929:0.153356:0.724929:0.136887:0.667844:0.136887:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.676819:0.156517:0.681773:0.156517:0.681773:0.146899:0.676819:0.146899:0.000000
1:@0.697936:0.156517:0.702889:0.156517:0.702889:0.146899:0.697936:0.146899:0.000000
:@0.717705:0.151216:0.724120:0.151216:0.724120:0.135398:0.717705:0.135398:0.000000
a b:@0.751091:0.153356:0.781184:0.153356:0.781184:0.136887:0.751091:0.136887:0.000000:0.000000:0.000000
2:@0.760067:0.156517:0.765020:0.156517:0.765020:0.146899:0.760067:0.146899:0.000000
2:@0.781184:0.156517:0.786137:0.156517:0.786137:0.146899:0.781184:0.146899:0.000000
Un producto escalar de   con   representado por   ∙   está definido :@0.404240:0.170591:0.895886:0.170591:0.895886:0.154094:0.404240:0.154094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.576123:0.170707:0.587393:0.170707:0.587393:0.154238:0.576123:0.154238:0.000000
:@0.579227:0.168567:0.585642:0.168567:0.585642:0.152749:0.579227:0.152749:0.000000
B:@0.621957:0.170707:0.631147:0.170707:0.631147:0.154238:0.621957:0.154238:0.000000
:@0.623941:0.168567:0.630357:0.168567:0.630357:0.152749:0.623941:0.152749:0.000000
A B:@0.763940:0.170707:0.795362:0.170707:0.795362:0.154238:0.763940:0.154238:0.000000:0.000000:0.000000
como   ∙   = :@0.404240:0.187942:0.500759:0.187942:0.500759:0.171444:0.404240:0.171444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B a a:@0.450169:0.188058:0.523661:0.188058:0.523661:0.171589:0.450169:0.171589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 2:@0.509731:0.191219:0.528614:0.191219:0.528614:0.181601:0.509731:0.181601:0.000000:0.000000:0.000000
 + :@0.528614:0.187942:0.547706:0.187942:0.547706:0.171444:0.528614:0.171444:0.000000:0.000000:0.000000
b b:@0.547706:0.188058:0.571191:0.188058:0.571191:0.171589:0.547706:0.171589:0.000000:0.000000:0.000000
1 2:@0.556973:0.191219:0.576145:0.191219:0.576145:0.181601:0.556973:0.181601:0.000000:0.000000:0.000000
. :@0.576144:0.187942:0.583041:0.187942:0.583041:0.171444:0.576144:0.171444:0.000000:0.000000
El número real   ∙   se llama producto escalar, producto punto o :@0.404240:0.222643:0.895946:0.222643:0.895946:0.206146:0.404240:0.206146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.517944:0.222759:0.553585:0.222759:0.553585:0.206290:0.517944:0.206290:0.000000:0.000000:0.000000
 :@0.521007:0.220619:0.552775:0.220619:0.552775:0.204801:0.521007:0.204801:0.000000:0.000000:0.000000
producto interior de   con   y es un número real.   :@0.404240:0.239994:0.770240:0.239994:0.770240:0.223497:0.404240:0.223497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.554315:0.240110:0.565585:0.240110:0.565585:0.223641:0.554315:0.223641:0.000000
:@0.557399:0.237970:0.563814:0.237970:0.563814:0.222152:0.557399:0.222152:0.000000
B:@0.600207:0.240110:0.609396:0.240110:0.609396:0.223641:0.600207:0.223641:0.000000
:@0.602172:0.237970:0.608587:0.237970:0.608587:0.222152:0.602172:0.222152:0.000000
Ejercicios resueltos:@0.404240:0.275072:0.534895:0.275072:0.534895:0.258285:0.404240:0.258285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404240:0.292263:0.416512:0.292263:0.416512:0.275549:0.404240:0.275549:0.000000:0.000000
  Sean   = (3, 5),   = (–1, 4). Entonces,   ·   = 3 · (–1) + 5 · 4 = 17. :@0.416512:0.292047:0.884581:0.292047:0.884581:0.275549:0.416512:0.275549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.465774:0.292162:0.477044:0.292162:0.477044:0.275693:0.465774:0.275693:0.000000
:@0.468856:0.290022:0.475271:0.290022:0.475271:0.274204:0.468856:0.274204:0.000000
B:@0.538211:0.292162:0.547400:0.292162:0.547400:0.275693:0.538211:0.275693:0.000000
:@0.540176:0.290022:0.546591:0.290022:0.546591:0.274204:0.540176:0.274204:0.000000
A B:@0.692950:0.292162:0.723832:0.292162:0.723832:0.275693:0.692950:0.275693:0.000000:0.000000:0.000000
 :@0.696032:0.290022:0.723023:0.290022:0.723023:0.274204:0.696032:0.274204:0.000000:0.000000:0.000000
2.:@0.404240:0.309614:0.416512:0.309614:0.416512:0.292900:0.404240:0.292900:0.000000:0.000000
  Sean   = (2, –1),   = (1, 2). Entonces,   ·   = 2 · 1 + (–1) · 2 = 0.:@0.416512:0.309397:0.871943:0.309397:0.871943:0.292900:0.416512:0.292900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.465774:0.309513:0.477044:0.309513:0.477044:0.293044:0.465774:0.293044:0.000000
:@0.468856:0.307373:0.475271:0.307373:0.475271:0.291555:0.468856:0.291555:0.000000
B:@0.548711:0.309513:0.557900:0.309513:0.557900:0.293044:0.548711:0.293044:0.000000
:@0.550676:0.307373:0.557091:0.307373:0.557091:0.291555:0.550676:0.291555:0.000000
A B:@0.692950:0.309513:0.723832:0.309513:0.723832:0.293044:0.692950:0.293044:0.000000:0.000000:0.000000
 :@0.696032:0.307373:0.723023:0.307373:0.723023:0.291555:0.696032:0.291555:0.000000:0.000000:0.000000
Teorema:@0.404240:0.344561:0.471185:0.344561:0.471185:0.327616:0.404240:0.327616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,  ,      ,      . El producto escalar en   arriba :@0.471187:0.344099:0.895917:0.344099:0.895917:0.327601:0.471187:0.327601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.516692:0.344214:0.561329:0.344214:0.561329:0.327746:0.516692:0.327746:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.519774:0.342075:0.561002:0.342075:0.561002:0.326256:0.519774:0.326256:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.565525:0.343580:0.580177:0.343580:0.580177:0.330207:0.565525:0.330207:0.000000
:@0.584720:0.343012:0.598025:0.343012:0.598025:0.330150:0.584720:0.330150:0.000000
2:@0.598025:0.337746:0.602978:0.337746:0.602978:0.328128:0.598025:0.328128:0.000000
α:@0.610276:0.351685:0.620853:0.351685:0.620853:0.332686:0.610276:0.332686:0.000000
:@0.625400:0.343580:0.640052:0.343580:0.640052:0.330207:0.625400:0.330207:0.000000
:@0.644596:0.343012:0.657901:0.343012:0.657901:0.330150:0.644596:0.330150:0.000000
:@0.828589:0.343012:0.841894:0.343012:0.841894:0.330150:0.828589:0.330150:0.000000
2:@0.841894:0.337746:0.846847:0.337746:0.846847:0.328128:0.841894:0.328128:0.000000
definido satisface las propiedades siguientes::@0.404229:0.361450:0.717996:0.361450:0.717996:0.344952:0.404229:0.344952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.404229:0.396368:0.414767:0.396368:0.414767:0.379653:0.404229:0.379653:0.000000:0.000000
 :@0.414767:0.396151:0.418909:0.396151:0.418909:0.379653:0.414767:0.379653:0.000000
A B:@0.427963:0.396267:0.458846:0.396267:0.458846:0.379798:0.427963:0.379798:0.000000:0.000000:0.000000
 :@0.431046:0.394127:0.458037:0.394127:0.458037:0.378309:0.431046:0.378309:0.000000:0.000000:0.000000
 ·   =   ·  . :@0.438617:0.396151:0.518722:0.396151:0.518722:0.379653:0.438617:0.379653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B A:@0.479055:0.396267:0.511671:0.396267:0.511671:0.379798:0.479055:0.379798:0.000000:0.000000:0.000000
 :@0.481020:0.394127:0.509899:0.394127:0.509899:0.378309:0.481020:0.378309:0.000000:0.000000:0.000000
ii):@0.665408:0.396368:0.680203:0.396368:0.680203:0.379653:0.665408:0.379653:0.000000:0.000000:0.000000
  (  +  ) ·   =   ·   +   ·  .:@0.680203:0.396151:0.865246:0.396151:0.865246:0.379653:0.680203:0.379653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C A C B C:@0.695095:0.396267:0.862819:0.396267:0.862819:0.379798:0.695095:0.379798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.698178:0.394127:0.704593:0.394127:0.704593:0.378309:0.698178:0.378309:0.000000
:@0.726806:0.394127:0.733221:0.394127:0.733221:0.378309:0.726806:0.378309:0.000000
:@0.755434:0.394127:0.761850:0.394127:0.761850:0.378309:0.755434:0.378309:0.000000
 :@0.784024:0.394127:0.812344:0.394127:0.812344:0.378309:0.784024:0.378309:0.000000:0.000000:0.000000
 :@0.833401:0.394127:0.862491:0.394127:0.862491:0.378309:0.833401:0.378309:0.000000:0.000000:0.000000
iii):@0.404229:0.420847:0.423282:0.420847:0.423282:0.404132:0.404229:0.404132:0.000000:0.000000:0.000000:0.000000
 (:@0.423282:0.420630:0.433916:0.420630:0.433916:0.404132:0.423282:0.404132:0.000000:0.000000
α :@0.433933:0.428216:0.448565:0.428216:0.448565:0.409217:0.433933:0.409217:0.000000:0.000000
A B:@0.448571:0.420745:0.485407:0.420745:0.485407:0.404276:0.448571:0.404276:0.000000:0.000000:0.000000
:@0.451654:0.418605:0.458069:0.418605:0.458069:0.402787:0.451654:0.402787:0.000000
) ·   =  (  ·  ). :@0.459225:0.420629:0.566998:0.420629:0.566998:0.404132:0.459225:0.404132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.478182:0.418605:0.484597:0.418605:0.484597:0.402787:0.478182:0.402787:0.000000
α:@0.505615:0.428216:0.516192:0.428216:0.516192:0.409217:0.505615:0.409217:0.000000
A B:@0.522149:0.420745:0.553031:0.420745:0.553031:0.404276:0.522149:0.404276:0.000000:0.000000:0.000000
 :@0.525231:0.418605:0.552222:0.418605:0.552222:0.402787:0.525231:0.402787:0.000000:0.000000:0.000000
iv):@0.665424:0.420846:0.684227:0.420846:0.684227:0.404132:0.665424:0.404132:0.000000:0.000000:0.000000
      ·   = 0     = 0,:@0.684227:0.420629:0.825745:0.420629:0.825745:0.404132:0.684227:0.404132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A A:@0.701585:0.420745:0.734548:0.420745:0.734548:0.404276:0.701585:0.404276:0.000000:0.000000:0.000000
 :@0.704668:0.418605:0.732776:0.418605:0.732776:0.402787:0.704668:0.402787:0.000000:0.000000:0.000000
A:@0.785654:0.420745:0.796924:0.420745:0.796924:0.404276:0.785654:0.404276:0.000000
:@0.788736:0.418605:0.795152:0.418605:0.795152:0.402787:0.788736:0.402787:0.000000
:@0.816671:0.418605:0.823086:0.418605:0.823086:0.402787:0.816671:0.402787:0.000000
 :@0.404240:0.437980:0.408382:0.437980:0.408382:0.421482:0.404240:0.421482:0.000000
 :@0.427985:0.437980:0.432127:0.437980:0.432127:0.421482:0.427985:0.421482:0.000000
 :@0.665419:0.437980:0.669561:0.437980:0.669561:0.421482:0.665419:0.421482:0.000000
     ·   > 0     ≠ 0.:@0.689154:0.437980:0.826708:0.437980:0.826708:0.421482:0.689154:0.421482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A A:@0.701580:0.438096:0.734543:0.438096:0.734543:0.421627:0.701580:0.421627:0.000000:0.000000:0.000000
 :@0.704663:0.435956:0.732771:0.435956:0.732771:0.420138:0.704663:0.420138:0.000000:0.000000:0.000000
A:@0.785654:0.438096:0.796924:0.438096:0.796924:0.421627:0.785654:0.421627:0.000000
:@0.788736:0.435956:0.795152:0.435956:0.795152:0.420138:0.788736:0.420138:0.000000
:@0.816671:0.435956:0.823086:0.435956:0.823086:0.420138:0.816671:0.420138:0.000000
 :@0.404240:0.455331:0.408382:0.455331:0.408382:0.438833:0.404240:0.438833:0.000000
Demostración:@0.404240:0.472899:0.509448:0.472899:0.509448:0.456184:0.404240:0.456184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean   = ( ,  ),   = ( ,  ), y   = ( ,  ) tres elemen-:@0.509448:0.472682:0.891774:0.472682:0.891774:0.456184:0.509448:0.456184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.553180:0.472797:0.564450:0.472797:0.564450:0.456329:0.553180:0.456329:0.000000
:@0.556282:0.470657:0.562697:0.470657:0.562697:0.454839:0.556282:0.454839:0.000000
a b B:@0.586779:0.472797:0.642918:0.472797:0.642918:0.456329:0.586779:0.456329:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.595765:0.475958:0.600718:0.475958:0.600718:0.466340:0.595765:0.466340:0.000000
1:@0.616409:0.475958:0.621362:0.475958:0.621362:0.466340:0.616409:0.466340:0.000000
:@0.635694:0.470657:0.642109:0.470657:0.642109:0.454839:0.635694:0.454839:0.000000
a b:@0.668117:0.472797:0.697755:0.472797:0.697755:0.456329:0.668117:0.456329:0.000000:0.000000:0.000000
2:@0.677121:0.475958:0.682074:0.475958:0.682074:0.466340:0.677121:0.466340:0.000000
2:@0.697763:0.475958:0.702716:0.475958:0.702716:0.466340:0.697763:0.466340:0.000000
C:@0.726587:0.472797:0.736624:0.472797:0.736624:0.456329:0.726587:0.456329:0.000000
:@0.729881:0.470657:0.736296:0.470657:0.736296:0.454839:0.729881:0.454839:0.000000
a b:@0.760378:0.472797:0.790004:0.472797:0.790004:0.456329:0.760378:0.456329:0.000000:0.000000:0.000000
3:@0.769370:0.475958:0.774323:0.475958:0.774323:0.466340:0.769370:0.466340:0.000000
3:@0.790012:0.475958:0.794965:0.475958:0.794965:0.466340:0.790012:0.466340:0.000000
tos de  .:@0.404247:0.490032:0.473180:0.490032:0.473180:0.473535:0.404247:0.473535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.452166:0.488945:0.465471:0.488945:0.465471:0.476083:0.452166:0.476083:0.000000
2:@0.465471:0.483679:0.470424:0.483679:0.470424:0.474061:0.465471:0.474061:0.000000
i):@0.404229:0.520425:0.414768:0.520425:0.414768:0.503711:0.404229:0.503711:0.000000:0.000000
  De la definición de producto escalar, se tiene::@0.414768:0.520208:0.748474:0.520208:0.748474:0.503711:0.414768:0.503711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404229:0.537559:0.408372:0.537559:0.408372:0.521061:0.404229:0.521061:0.000000
A B:@0.427964:0.537675:0.458846:0.537675:0.458846:0.521206:0.427964:0.521206:0.000000:0.000000:0.000000
 :@0.431047:0.535535:0.458037:0.535535:0.458037:0.519717:0.431047:0.519717:0.000000:0.000000:0.000000
 ·   = :@0.438618:0.537559:0.479056:0.537559:0.479056:0.521061:0.438618:0.521061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a a:@0.479056:0.537675:0.501978:0.537674:0.501978:0.521205:0.479056:0.521206:0.000000:0.000000:0.000000
1 2:@0.488047:0.540835:0.506931:0.540835:0.506931:0.531217:0.488047:0.531217:0.000000:0.000000:0.000000
 + :@0.506930:0.537558:0.526022:0.537558:0.526022:0.521061:0.506930:0.521061:0.000000:0.000000:0.000000
b b:@0.526022:0.537674:0.549509:0.537674:0.549509:0.521205:0.526022:0.521205:0.000000:0.000000:0.000000
1 2:@0.535289:0.540835:0.554461:0.540835:0.554461:0.531217:0.535289:0.531217:0.000000:0.000000:0.000000
 = :@0.554462:0.537558:0.573553:0.537558:0.573553:0.521061:0.554462:0.521061:0.000000:0.000000:0.000000
a a:@0.573553:0.537674:0.596462:0.537674:0.596462:0.521205:0.573553:0.521205:0.000000:0.000000:0.000000
2 1:@0.582530:0.540835:0.601413:0.540835:0.601413:0.531217:0.582530:0.531217:0.000000:0.000000:0.000000
 + :@0.601414:0.537558:0.620505:0.537558:0.620505:0.521061:0.601414:0.521061:0.000000:0.000000:0.000000
b b:@0.620505:0.537674:0.643991:0.537674:0.643991:0.521205:0.620505:0.521205:0.000000:0.000000:0.000000
2 1:@0.629772:0.540835:0.648945:0.540835:0.648945:0.531217:0.629772:0.531217:0.000000:0.000000:0.000000
 =   ·  .:@0.648943:0.537558:0.703560:0.537558:0.703560:0.521061:0.648943:0.521061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B A:@0.668035:0.537674:0.700651:0.537674:0.700651:0.521205:0.668035:0.521205:0.000000:0.000000:0.000000
 :@0.670000:0.535534:0.698879:0.535534:0.698879:0.519716:0.670000:0.519716:0.000000:0.000000:0.000000
ii):@0.404236:0.567951:0.419032:0.567951:0.419032:0.551237:0.404236:0.551237:0.000000:0.000000:0.000000
  Primeramente,   +   = ( ,  ) + ( ,  ) = (  +  ,   +  ).:@0.419032:0.567734:0.843578:0.567734:0.843578:0.551236:0.419032:0.551237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.536300:0.567850:0.575235:0.567850:0.575235:0.551381:0.536300:0.551381:0.000000:0.000000:0.000000
:@0.539382:0.565710:0.545797:0.565710:0.545797:0.549892:0.539382:0.549892:0.000000
:@0.568010:0.565710:0.574425:0.565710:0.574425:0.549892:0.568010:0.549892:0.000000
a b:@0.601397:0.567850:0.631497:0.567849:0.631497:0.551381:0.601397:0.551381:0.000000:0.000000:0.000000
1:@0.610381:0.571010:0.615334:0.571010:0.615334:0.561392:0.610381:0.561392:0.000000
1:@0.631496:0.571010:0.636449:0.571010:0.636449:0.561392:0.631496:0.561392:0.000000
a b:@0.667447:0.567849:0.697541:0.567849:0.697541:0.551381:0.667447:0.551381:0.000000:0.000000:0.000000
2:@0.676424:0.571010:0.681377:0.571010:0.681377:0.561392:0.676424:0.561392:0.000000
2:@0.697540:0.571010:0.702494:0.571010:0.702494:0.561392:0.697540:0.561392:0.000000
a:@0.733492:0.567849:0.742470:0.567849:0.742470:0.551381:0.733492:0.551381:0.000000
1:@0.742467:0.571010:0.747420:0.571010:0.747420:0.561392:0.742467:0.561392:0.000000
a b:@0.766513:0.567849:0.796607:0.567849:0.796607:0.551381:0.766513:0.551381:0.000000:0.000000:0.000000
2:@0.775489:0.571010:0.780443:0.571010:0.780443:0.561392:0.775489:0.561392:0.000000
1:@0.796606:0.571010:0.801559:0.571010:0.801559:0.561392:0.796606:0.561392:0.000000
b:@0.820651:0.567849:0.829918:0.567849:0.829918:0.551381:0.820651:0.551381:0.000000
2:@0.829916:0.571010:0.834869:0.571010:0.834869:0.561392:0.829916:0.561392:0.000000
 :@0.404234:0.585084:0.408376:0.585084:0.408376:0.568587:0.404234:0.568587:0.000000
Luego, por la definición del producto escalar en  , obtenemos:@0.427968:0.585084:0.876406:0.585084:0.876406:0.568587:0.427968:0.568587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.769990:0.583997:0.783294:0.583997:0.783294:0.571135:0.769990:0.571135:0.000000
2:@0.783294:0.578731:0.788248:0.578731:0.788248:0.569113:0.783294:0.569113:0.000000
 :@0.404234:0.605992:0.408376:0.605992:0.408376:0.589494:0.404234:0.589494:0.000000
A C a a:@0.427968:0.606108:0.501382:0.606115:0.501382:0.589647:0.427968:0.589639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.431051:0.603968:0.459371:0.603968:0.459371:0.588150:0.431051:0.588150:0.000000:0.000000:0.000000
 ·   = :@0.438622:0.605992:0.478463:0.605992:0.478463:0.589494:0.438622:0.589494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 3:@0.487450:0.609276:0.506333:0.609276:0.506333:0.599658:0.487450:0.599658:0.000000:0.000000:0.000000
 + :@0.506334:0.606000:0.525426:0.606000:0.525426:0.589502:0.506334:0.589502:0.000000:0.000000:0.000000
b b:@0.525426:0.606115:0.548911:0.606115:0.548911:0.589647:0.525426:0.589647:0.000000:0.000000:0.000000
1 3:@0.534692:0.609276:0.553865:0.609276:0.553865:0.599658:0.534692:0.599658:0.000000:0.000000:0.000000
,       ·   = :@0.554426:0.606000:0.635302:0.606000:0.635302:0.589502:0.554426:0.589502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B C a a:@0.585155:0.606115:0.658216:0.606115:0.658216:0.589647:0.585155:0.589647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.587120:0.603975:0.616210:0.603975:0.616210:0.588157:0.587120:0.588157:0.000000:0.000000:0.000000
2 3:@0.644286:0.609276:0.663169:0.609276:0.663169:0.599658:0.644286:0.599658:0.000000:0.000000:0.000000
 + :@0.663170:0.606000:0.682261:0.606000:0.682261:0.589502:0.663170:0.589502:0.000000:0.000000:0.000000
b b:@0.682261:0.606115:0.705747:0.606115:0.705747:0.589647:0.682261:0.589647:0.000000:0.000000:0.000000
2 3:@0.691528:0.609276:0.710699:0.609276:0.710699:0.599658:0.691528:0.599658:0.000000:0.000000:0.000000
, entonces:@0.711261:0.606000:0.782868:0.606000:0.782868:0.589502:0.711261:0.589502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) ·  = (  +  )  + (  +  )  = :@0.427965:0.636175:0.705078:0.636175:0.705078:0.619677:0.427965:0.619678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.433918:0.636291:0.501000:0.636291:0.501000:0.619822:0.433918:0.619822:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.437001:0.634151:0.443416:0.634151:0.443416:0.618333:0.437001:0.618333:0.000000
:@0.465629:0.634151:0.472044:0.634151:0.472044:0.618333:0.465629:0.618333:0.000000
 :@0.494257:0.634151:0.505489:0.634151:0.505489:0.618333:0.494257:0.618333:0.000000:0.000000
a:@0.526391:0.636291:0.535369:0.636291:0.535369:0.619822:0.526391:0.619822:0.000000
1:@0.535381:0.639451:0.540334:0.639451:0.540334:0.629833:0.535381:0.629833:0.000000
a a:@0.559426:0.636290:0.588287:0.636290:0.588287:0.619822:0.559426:0.619822:0.000000:0.000000:0.000000
2:@0.568403:0.639451:0.573356:0.639451:0.573356:0.629833:0.568403:0.629833:0.000000
3:@0.588286:0.639451:0.593240:0.639451:0.593240:0.629833:0.588286:0.629833:0.000000
b:@0.618285:0.636290:0.627551:0.636290:0.627551:0.619822:0.618285:0.619822:0.000000
1:@0.627551:0.639451:0.632504:0.639451:0.632504:0.629833:0.627551:0.629833:0.000000
b b:@0.651595:0.636290:0.681034:0.636290:0.681034:0.619822:0.651595:0.619822:0.000000:0.000000:0.000000
2:@0.660861:0.639451:0.665814:0.639451:0.665814:0.629833:0.660861:0.629833:0.000000
3:@0.681033:0.639451:0.685986:0.639451:0.685986:0.629833:0.681033:0.629833:0.000000
a a:@0.705078:0.636290:0.727986:0.636290:0.727986:0.619822:0.705078:0.619822:0.000000:0.000000:0.000000
1 3:@0.714055:0.639451:0.732939:0.639451:0.732939:0.629833:0.714055:0.629833:0.000000:0.000000:0.000000
 + :@0.732938:0.636175:0.752030:0.636175:0.752030:0.619677:0.732938:0.619677:0.000000:0.000000:0.000000
a a:@0.752030:0.636290:0.774938:0.636290:0.774938:0.619822:0.752030:0.619822:0.000000:0.000000:0.000000
2 3:@0.761007:0.639451:0.779891:0.639451:0.779891:0.629833:0.761007:0.629833:0.000000:0.000000:0.000000
 + :@0.779890:0.636175:0.798982:0.636175:0.798982:0.619677:0.779890:0.619677:0.000000:0.000000:0.000000
b b:@0.798982:0.636290:0.822469:0.636290:0.822469:0.619822:0.798982:0.619822:0.000000:0.000000:0.000000
1 3:@0.808249:0.639451:0.827421:0.639451:0.827421:0.629833:0.808249:0.629833:0.000000:0.000000:0.000000
 + :@0.827983:0.636175:0.847075:0.636175:0.847075:0.619677:0.827983:0.619677:0.000000:0.000000:0.000000
b b:@0.847075:0.636290:0.870560:0.636290:0.870560:0.619822:0.847075:0.619822:0.000000:0.000000:0.000000
2 3:@0.856341:0.639451:0.875514:0.639451:0.875514:0.629833:0.856341:0.629833:0.000000:0.000000:0.000000
= :@0.506334:0.660653:0.521284:0.660653:0.521284:0.644156:0.506334:0.644156:0.000000:0.000000
a a:@0.521284:0.660769:0.544191:0.660769:0.544191:0.644300:0.521284:0.644300:0.000000:0.000000:0.000000
1 3:@0.530261:0.663930:0.549144:0.663930:0.549144:0.654312:0.530261:0.654312:0.000000:0.000000:0.000000
 + :@0.549144:0.660653:0.568236:0.660653:0.568236:0.644156:0.549144:0.644156:0.000000:0.000000:0.000000
b b:@0.568236:0.660769:0.591721:0.660769:0.591721:0.644300:0.568236:0.644300:0.000000:0.000000:0.000000
1 3:@0.577501:0.663930:0.596674:0.663930:0.596674:0.654312:0.577501:0.654312:0.000000:0.000000:0.000000
 + :@0.597236:0.660653:0.616327:0.660653:0.616327:0.644156:0.597236:0.644156:0.000000:0.000000:0.000000
a a:@0.616327:0.660769:0.639235:0.660769:0.639235:0.644300:0.616327:0.644300:0.000000:0.000000:0.000000
2 3:@0.625304:0.663930:0.644189:0.663930:0.644189:0.654312:0.625304:0.654312:0.000000:0.000000:0.000000
 + :@0.644189:0.660653:0.663281:0.660653:0.663281:0.644156:0.644189:0.644156:0.000000:0.000000:0.000000
b b:@0.663281:0.660769:0.686766:0.660769:0.686766:0.644300:0.663281:0.644300:0.000000:0.000000:0.000000
2 3:@0.672546:0.663930:0.691719:0.663930:0.691719:0.654312:0.672546:0.654312:0.000000:0.000000:0.000000
   :@0.692280:0.658630:0.743449:0.658630:0.743449:0.642812:0.692280:0.642812:0.000000:0.000000:0.000000:0.000000:0.000000
=   ·   +   ·  .:@0.697097:0.660654:0.796351:0.660654:0.796351:0.644157:0.697097:0.644157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A C B C:@0.712046:0.660770:0.793924:0.660770:0.793924:0.644301:0.712046:0.644301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.764506:0.658630:0.793596:0.658630:0.793596:0.642812:0.764506:0.642812:0.000000:0.000000:0.000000
 :@0.404245:0.690830:0.408387:0.690830:0.408387:0.674333:0.404245:0.674333:0.000000
Después, (  +  ) ·  =   ·   +   ·  .:@0.427980:0.690830:0.672379:0.690830:0.672379:0.674333:0.427980:0.674333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.501554:0.690946:0.568636:0.690946:0.568636:0.674477:0.501554:0.674477:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.504637:0.688806:0.511052:0.688806:0.511052:0.672988:0.504637:0.672988:0.000000
:@0.533265:0.688806:0.539680:0.688806:0.539680:0.672988:0.533265:0.672988:0.000000
   :@0.561893:0.688806:0.619477:0.688806:0.619477:0.672988:0.561893:0.672988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A C B C:@0.588074:0.690946:0.669952:0.690946:0.669952:0.674477:0.588074:0.674477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.640534:0.688806:0.669624:0.688806:0.669624:0.672988:0.640534:0.672988:0.000000:0.000000:0.000000
Las otras propiedades se proponen al estudiante para que investiguen :@0.404245:0.725532:0.895947:0.725532:0.895947:0.709034:0.404245:0.709034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y demuestren.:@0.404245:0.742883:0.504155:0.742883:0.504155:0.726385:0.404245:0.726385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Longitud o norma de un vector:@0.404236:0.778980:0.654051:0.778980:0.654051:0.761297:0.404236:0.761297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el caso del producto escalar habitual, esta norma coincide con la :@0.404236:0.795687:0.895997:0.795687:0.895997:0.779190:0.404236:0.779190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
longitud del vector.:@0.404236:0.813038:0.541480:0.813038:0.541480:0.796540:0.404236:0.796540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.404236:0.848202:0.484320:0.848202:0.484320:0.831256:0.404236:0.831256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sea   = ( ,  )    . La longitud o norma de  , que se:@0.484322:0.847740:0.870339:0.847740:0.870339:0.831242:0.484322:0.831242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.519481:0.847855:0.530751:0.847855:0.530751:0.831387:0.519481:0.831387:0.000000
a b:@0.555796:0.847855:0.580937:0.847855:0.580937:0.831387:0.555796:0.831387:0.000000:0.000000:0.000000
:@0.591029:0.847221:0.605681:0.847221:0.605681:0.833848:0.591029:0.833848:0.000000
:@0.609822:0.846653:0.623126:0.846653:0.623126:0.833790:0.609822:0.833790:0.000000
2:@0.623126:0.841387:0.628080:0.841387:0.628080:0.831768:0.623126:0.831768:0.000000
A:@0.807072:0.847855:0.818342:0.847855:0.818342:0.831387:0.807072:0.831387:0.000000
:@0.810156:0.845715:0.816571:0.845715:0.816571:0.829897:0.810156:0.829897:0.000000
denota || ||, se define como || || =   (  ·  ) =      +   .:@0.404237:0.872219:0.805123:0.872218:0.805123:0.855720:0.404237:0.855721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.471781:0.872334:0.483051:0.872334:0.483051:0.855866:0.471781:0.855866:0.000000
:@0.474863:0.870194:0.481279:0.870194:0.481279:0.854376:0.474863:0.854376:0.000000
A:@0.626308:0.872334:0.637578:0.872334:0.637578:0.855866:0.626308:0.855866:0.000000
:@0.629390:0.870194:0.635805:0.870194:0.635805:0.854376:0.629390:0.854376:0.000000
A A:@0.681464:0.872334:0.714427:0.872334:0.714427:0.855866:0.681464:0.855866:0.000000:0.000000:0.000000
 :@0.684547:0.870194:0.712655:0.870194:0.712655:0.854376:0.684547:0.854376:0.000000:0.000000:0.000000
a:@0.751281:0.872334:0.760259:0.872334:0.760259:0.855866:0.751281:0.855866:0.000000
2:@0.760250:0.865866:0.765203:0.865866:0.765203:0.856248:0.760250:0.856248:0.000000
a:@0.784295:0.872334:0.793273:0.872334:0.793273:0.855865:0.784295:0.855865:0.000000
2:@0.793272:0.865866:0.798225:0.865866:0.798225:0.856248:0.793272:0.856248:0.000000
Para todo   = ( ,  )    , por la propiedad iv) de la definición de pro-:@0.404232:0.906919:0.891790:0.906919:0.891790:0.890422:0.404232:0.890422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.476438:0.907035:0.487708:0.907035:0.487708:0.890566:0.476438:0.890566:0.000000
a b:@0.511212:0.907035:0.535563:0.907035:0.535563:0.890566:0.511212:0.890566:0.000000:0.000000:0.000000
:@0.544899:0.906401:0.559552:0.906401:0.559552:0.893028:0.544899:0.893028:0.000000
:@0.562920:0.905833:0.576225:0.905833:0.576225:0.892970:0.562920:0.892970:0.000000
2:@0.576225:0.900568:0.581178:0.900568:0.581178:0.890950:0.576225:0.890950:0.000000
ducto escalar, se tiene   ·   ≥ 0, con lo cual || || está bien definido.:@0.404227:0.924270:0.880075:0.924270:0.880075:0.907773:0.404227:0.907773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A A:@0.563200:0.924386:0.596167:0.924386:0.596167:0.907917:0.563200:0.907917:0.000000:0.000000:0.000000
 :@0.566286:0.922246:0.594394:0.922246:0.594394:0.906428:0.566286:0.906428:0.000000:0.000000:0.000000
A:@0.724107:0.924386:0.735377:0.924386:0.735377:0.907917:0.724107:0.907917:0.000000
:@0.727190:0.922246:0.733605:0.922246:0.733605:0.906428:0.727190:0.906428:0.000000
Saberes previos:@0.199646:0.097890:0.307805:0.097890:0.307805:0.082418:0.199646:0.082418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es el producto :@0.199884:0.126518:0.334658:0.126518:0.334658:0.111455:0.199884:0.111455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
escalar de vectores?:@0.153341:0.142360:0.280567:0.142360:0.280567:0.127297:0.153341:0.127297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.189470:0.363493:0.189470:0.363493:0.173997:0.199646:0.173997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿El producto escalar de :@0.199884:0.218097:0.353124:0.218097:0.353124:0.203034:0.199884:0.203034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectores tiene aplicaciones en :@0.153341:0.233939:0.350416:0.233939:0.350416:0.218876:0.153341:0.218876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la física? :@0.153341:0.249781:0.208378:0.249781:0.208378:0.234718:0.153341:0.234718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interculturalidad:@0.199644:0.707500:0.319958:0.707500:0.319958:0.692028:0.199644:0.692028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una de las mayores ma-:@0.193071:0.735431:0.348301:0.735431:0.348301:0.720368:0.193071:0.720368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nifestaciones de la cultura de :@0.153335:0.751273:0.345045:0.751273:0.345045:0.736210:0.153335:0.736210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un pueblo está en la música y la :@0.153335:0.767115:0.363549:0.767115:0.363549:0.752052:0.153335:0.752052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
danza. Ecuador tiene una rique-:@0.153335:0.782957:0.358835:0.782957:0.358835:0.767894:0.153335:0.767894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
za cultural muy diversa en cada :@0.153335:0.798799:0.360192:0.798799:0.360192:0.783736:0.153335:0.783736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una de sus regiones. Así, en :@0.153335:0.814641:0.332837:0.814641:0.332837:0.799578:0.153335:0.799578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esmeraldas y el Carchi, existen :@0.153335:0.830483:0.351588:0.830483:0.351588:0.815420:0.153335:0.815420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
asentamientos afroecuatorianos :@0.153335:0.846325:0.364520:0.846325:0.364520:0.831262:0.153335:0.831262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que hacen música con la ma-:@0.153335:0.862167:0.343061:0.862167:0.343061:0.847104:0.153335:0.847104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rimba, un instrumento traído :@0.153335:0.878009:0.346770:0.878009:0.346770:0.862946:0.153335:0.862946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del África por los esclavos, que :@0.153335:0.893851:0.355194:0.893851:0.355194:0.878788:0.153335:0.878788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
utiliza una escala pentatónica.:@0.153335:0.909693:0.347842:0.909693:0.347842:0.894630:0.153335:0.894630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.527715:0.297267:0.527715:0.297267:0.512243:0.199644:0.512243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199644:0.540283:0.311603:0.540283:0.311603:0.524811:0.199644:0.524811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la siguiente :@0.193071:0.564758:0.329536:0.564758:0.329536:0.549695:0.193071:0.549695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simbología matemática::@0.153335:0.580600:0.308107:0.580600:0.308107:0.565536:0.153335:0.565536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A un producto escalar de   con :@0.153335:0.603570:0.363313:0.603569:0.363313:0.588506:0.153335:0.588507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.322469:0.603675:0.332759:0.603675:0.332759:0.588639:0.322469:0.588639:0.000000
:@0.325284:0.601721:0.331141:0.601721:0.331141:0.587279:0.325284:0.587279:0.000000
B:@0.153344:0.619517:0.161734:0.619517:0.161734:0.604481:0.153344:0.604481:0.000000
:@0.155578:0.617563:0.161435:0.617563:0.161435:0.603121:0.155578:0.603121:0.000000
 lo denotamos por   ·  .:@0.161434:0.619411:0.315888:0.619411:0.315888:0.604348:0.161434:0.604348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.286532:0.619517:0.313672:0.619517:0.313672:0.604481:0.286532:0.604481:0.000000:0.000000:0.000000
 :@0.289346:0.617563:0.313373:0.617563:0.313373:0.603121:0.289346:0.603121:0.000000:0.000000:0.000000
Sea   = ( ,  ) :@0.153339:0.642382:0.244473:0.642382:0.244473:0.627319:0.153339:0.627319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.179143:0.642488:0.189434:0.642488:0.189434:0.627451:0.179143:0.627451:0.000000
a b:@0.212301:0.642488:0.235256:0.642488:0.235256:0.627451:0.212301:0.627451:0.000000:0.000000:0.000000
:@0.244475:0.642033:0.258430:0.642033:0.258430:0.629297:0.244475:0.629297:0.000000
 :@0.258430:0.642184:0.262828:0.642184:0.262828:0.628811:0.258430:0.628811:0.000000
:@0.262828:0.641379:0.274923:0.641379:0.274923:0.629687:0.262828:0.629687:0.000000
2:@0.274923:0.636581:0.279445:0.636581:0.279445:0.627800:0.274923:0.627800:0.000000
. La longitud :@0.279444:0.642382:0.363065:0.642382:0.363065:0.627319:0.279444:0.627319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o norma de   se denota ||   ||.:@0.153341:0.658224:0.350136:0.658224:0.350136:0.643161:0.153341:0.643161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.233149:0.658330:0.243439:0.658330:0.243439:0.643294:0.233149:0.643294:0.000000
:@0.235963:0.656376:0.241821:0.656376:0.241821:0.641934:0.235963:0.641934:0.000000
A:@0.326021:0.658330:0.336311:0.658330:0.336311:0.643294:0.326021:0.643294:0.000000
:@0.328835:0.656376:0.334692:0.656376:0.334692:0.641934:0.328835:0.641934:0.000000
Competencia :@0.199644:0.299978:0.297267:0.299978:0.297267:0.284505:0.199644:0.284505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.312546:0.283707:0.312546:0.283707:0.297073:0.199644:0.297073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El producto escalar en :@0.199880:0.337020:0.347600:0.337020:0.347600:0.321957:0.199880:0.321957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.153344:0.351859:0.165439:0.351859:0.165439:0.340167:0.153344:0.340167:0.000000
2:@0.165439:0.347061:0.169961:0.347061:0.169961:0.338280:0.165439:0.338280:0.000000
 que hemos definido es el :@0.169961:0.352862:0.339806:0.352862:0.339806:0.337799:0.169961:0.337799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
más utilizado. Cabe precisar :@0.153338:0.368704:0.337152:0.368704:0.337152:0.353641:0.153338:0.353641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que un producto escalar en   :@0.153338:0.384546:0.356412:0.384546:0.356412:0.369483:0.153338:0.369483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.336014:0.383543:0.348109:0.383543:0.348109:0.371851:0.336014:0.371851:0.000000
2:@0.348107:0.378745:0.352629:0.378745:0.352629:0.369964:0.348107:0.369964:0.000000
es una función::@0.153336:0.400388:0.251345:0.400388:0.251345:0.385325:0.153336:0.385325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
· ::@0.154389:0.430531:0.163202:0.430531:0.163202:0.415468:0.154389:0.415468:0.000000:0.000000:0.000000
 :@0.153344:0.422006:0.157486:0.422006:0.157486:0.405508:0.153344:0.405508:0.000000
:@0.177087:0.420683:0.189182:0.420683:0.189182:0.408990:0.177087:0.408990:0.000000
2:@0.189182:0.415886:0.193704:0.415886:0.193704:0.407105:0.189182:0.407105:0.000000
 ×  , :@0.193704:0.422006:0.237166:0.422006:0.237166:0.405508:0.193704:0.405508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.213653:0.420683:0.225748:0.420683:0.225748:0.408990:0.213653:0.408990:0.000000
2:@0.225748:0.415886:0.230270:0.415886:0.230270:0.407105:0.225748:0.407105:0.000000
→ :@0.237166:0.429593:0.256663:0.429593:0.256663:0.410594:0.237166:0.410594:0.000000:0.000000
:@0.256664:0.420683:0.268760:0.420683:0.268760:0.408990:0.256664:0.408990:0.000000
,:@0.268760:0.422006:0.271514:0.422006:0.271514:0.405508:0.268760:0.405508:0.000000
(:@0.177076:0.439357:0.183029:0.439357:0.183029:0.422859:0.177076:0.422859:0.000000
A B:@0.183041:0.439142:0.207805:0.439142:0.207805:0.424106:0.183041:0.424106:0.000000:0.000000:0.000000
 :@0.185855:0.437188:0.207506:0.437188:0.207506:0.422746:0.185855:0.422746:0.000000:0.000000:0.000000
, :@0.193119:0.439036:0.199416:0.439036:0.199416:0.423973:0.193119:0.423973:0.000000:0.000000
)        :@0.207506:0.439357:0.257315:0.439357:0.257315:0.422859:0.207506:0.422859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.237732:0.446943:0.253175:0.446943:0.253175:0.427944:0.237732:0.427944:0.000000
A B:@0.257314:0.439142:0.284455:0.439142:0.284455:0.424106:0.257314:0.424106:0.000000:0.000000:0.000000
 :@0.260129:0.437188:0.284156:0.437188:0.284156:0.422746:0.260129:0.422746:0.000000:0.000000:0.000000
 ·  ,:@0.265985:0.439036:0.286670:0.439036:0.286670:0.423973:0.265985:0.423973:0.000000:0.000000:0.000000:0.000000:0.000000
y satisface las propiedades del :@0.153338:0.462799:0.349727:0.462799:0.349727:0.447736:0.153338:0.447736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
teorema adyacente.:@0.153338:0.478641:0.280352:0.478641:0.280352:0.463578:0.153338:0.463578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000