159:@0.918240:0.967835:0.943652:0.967835:0.943652:0.951847:0.918240:0.951847:0.000000:0.000000:0.000000
En la figura 3.26. se muestran el vector  , el vector :@0.108233:0.101261:0.467837:0.101261:0.467837:0.084763:0.108233:0.084763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.381634:0.101377:0.392904:0.101377:0.392904:0.084908:0.381634:0.084908:0.000000
B    S:@0.469901:0.101754:0.515259:0.101377:0.515259:0.084908:0.469901:0.085285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.487710:0.101044:0.503758:0.101044:0.503758:0.086397:0.487710:0.086397:0.000000
 y la recta  .  :@0.515259:0.101261:0.599911:0.101261:0.599911:0.084763:0.515259:0.084763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.585094:0.101377:0.592973:0.101377:0.592973:0.084908:0.585094:0.084908:0.000000
Obsérvese que el símbolo :@0.108242:0.118612:0.302684:0.118612:0.302684:0.102114:0.108242:0.102114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.304919:0.117643:0.325784:0.117643:0.325784:0.104196:0.304919:0.104196:0.000000:0.000000
ha sido dibujado para indicar que el :@0.328425:0.118612:0.599866:0.118612:0.599866:0.102114:0.328425:0.102114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector   y el conjunto   forman un ángulo recto en el punto  .:@0.108242:0.137842:0.564137:0.137849:0.564137:0.121351:0.108242:0.121345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.161750:0.137964:0.173020:0.137964:0.173020:0.121496:0.161750:0.121496:0.000000
S:@0.277913:0.137964:0.285793:0.137964:0.285793:0.121496:0.277913:0.121496:0.000000
O:@0.549476:0.137964:0.561382:0.137964:0.561382:0.121496:0.549476:0.121496:0.000000
Ángulo entre dos vectores:@0.108233:0.174702:0.317480:0.174702:0.317480:0.157019:0.108233:0.157019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108233:0.199001:0.188317:0.199001:0.188317:0.182055:0.108233:0.182055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.108233:0.224897:0.146031:0.224897:0.146031:0.208400:0.108233:0.208400:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.147975:0.224103:0.175136:0.224103:0.175136:0.208382:0.147975:0.208382:0.000000:0.000000
,:@0.159726:0.223992:0.162355:0.223992:0.162355:0.208244:0.159726:0.208244:0.000000
2:@0.206292:0.216321:0.210986:0.216321:0.210986:0.207206:0.206292:0.207206:0.000000
∈:@0.179007:0.224599:0.192119:0.224599:0.192119:0.209059:0.179007:0.209059:0.000000
 no nulos. El ángulo :@0.214787:0.224903:0.350915:0.224903:0.350915:0.208405:0.214787:0.208405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
θ:@0.349378:0.225539:0.359415:0.225539:0.364188:0.209258:0.354150:0.209258:0.000000
π:@0.397599:0.225539:0.408176:0.225539:0.412948:0.209258:0.402371:0.209258:0.000000
[:@0.378024:0.228730:0.384439:0.228730:0.384439:0.205612:0.378024:0.205612:0.000000
]:@0.412412:0.228730:0.418828:0.228730:0.418828:0.205612:0.412412:0.205612:0.000000
∈:@0.365513:0.225539:0.379249:0.225539:0.379249:0.209258:0.365513:0.209258:0.000000
0,:@0.385568:0.224903:0.398225:0.224903:0.398225:0.208405:0.385568:0.208405:0.000000:0.000000
 entre los vectores   y   :@0.421324:0.224903:0.599910:0.224903:0.599910:0.208405:0.421324:0.208405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.551409:0.225019:0.590770:0.225396:0.590770:0.208927:0.551409:0.208550:0.000000:0.000000:0.000000
 :@0.595768:0.224903:0.599910:0.224903:0.599910:0.208405:0.595768:0.208405:0.000000
se define como cos( ):@0.108241:0.252939:0.268909:0.252941:0.268909:0.236443:0.108241:0.236441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
θ:@0.250172:0.253577:0.260209:0.253577:0.264982:0.237296:0.254944:0.237296:0.000000
=:@0.272222:0.253577:0.282799:0.253577:0.282799:0.237296:0.272222:0.237296:0.000000
⋅:@0.309809:0.244265:0.314625:0.244265:0.314625:0.227985:0.309809:0.227985:0.000000
AB:@0.296940:0.243745:0.325086:0.243745:0.325086:0.227276:0.296940:0.227276:0.000000:0.000000
AB:@0.294628:0.264493:0.327379:0.264493:0.327379:0.248025:0.294628:0.248025:0.000000:0.000000
.:@0.337031:0.252941:0.339786:0.252941:0.339786:0.236443:0.337031:0.236443:0.000000
De la definición del ángulo entre los vectores :@0.108233:0.289528:0.444720:0.289528:0.444720:0.273030:0.108233:0.273030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.450319:0.289644:0.461589:0.289644:0.461589:0.273175:0.450319:0.273175:0.000000
 y  , se sigue que :@0.465029:0.289528:0.599926:0.289528:0.599926:0.273030:0.465029:0.273030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.487542:0.290021:0.496732:0.290021:0.496732:0.273552:0.487542:0.273552:0.000000
⊥⊥:@0.126451:0.316945:0.144589:0.316945:0.144589:0.300664:0.126451:0.300664:0.000000:0.000000
⋅⋅:@0.193783:0.316945:0.204061:0.316945:0.204061:0.300664:0.193783:0.300664:0.000000:0.000000
AA:@0.111945:0.316424:0.128676:0.316424:0.128676:0.299956:0.111945:0.299956:0.000000:0.000000
BB:@0.142942:0.316424:0.157593:0.316424:0.157593:0.299956:0.142942:0.299956:0.000000:0.000000
ABAB:@0.180895:0.316424:0.214503:0.316424:0.214503:0.299956:0.180895:0.299956:0.000000:0.000000:0.000000:0.000000
=0=0, con lo cual  cos( )= 0,  de donde  =:@0.212933:0.316309:0.517398:0.316309:0.517398:0.299811:0.212933:0.299811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.155718:0.316309:0.159860:0.316309:0.159860:0.299811:0.155718:0.299811:0.000000
⇔:@0.159860:0.316858:0.179934:0.316858:0.179934:0.298018:0.159860:0.298018:0.000000
 :@0.179934:0.316309:0.184076:0.316309:0.184076:0.299811:0.179934:0.299811:0.000000
θ:@0.363651:0.316568:0.373688:0.316568:0.378461:0.300287:0.368423:0.300287:0.000000
θ:@0.490455:0.316945:0.500492:0.316945:0.505265:0.300664:0.495227:0.300664:0.000000
π:@0.519720:0.307633:0.530296:0.307633:0.535069:0.291352:0.524492:0.291352:0.000000
2:@0.523185:0.327271:0.531681:0.327271:0.531681:0.310773:0.523185:0.310773:0.000000
.:@0.536796:0.316309:0.539551:0.316309:0.539551:0.299811:0.536796:0.299811:0.000000
Por este motivo, dos vectores perpendiculares u ortogonales forman :@0.108241:0.340788:0.599907:0.340788:0.599907:0.324290:0.108241:0.324290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un ángulo recto.:@0.108241:0.358138:0.224054:0.358138:0.224054:0.341640:0.108241:0.341641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.108233:0.382993:0.226211:0.382993:0.226211:0.366206:0.108233:0.366206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vértices de un triángulo son los puntos :@0.108233:0.411492:0.430142:0.411492:0.430142:0.394994:0.108233:0.394994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.462818:0.414432:0.498979:0.414432:0.498979:0.392452:0.462818:0.392452:0.000000:0.000000:0.000000
=0,0 ,   =:@0.449938:0.411496:0.539147:0.411496:0.539147:0.394999:0.449938:0.394999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.435855:0.411612:0.447126:0.411612:0.447126:0.395143:0.435855:0.395143:0.000000
( ):@0.541217:0.418243:0.587627:0.418243:0.587627:0.388123:0.541217:0.388123:0.000000:0.000000:0.000000
,0,  :@0.567448:0.411496:0.599915:0.411496:0.599915:0.394999:0.567448:0.394999:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.557708:0.403932:0.562626:0.403932:0.562626:0.394383:0.557708:0.394383:0.000000
2:@0.554252:0.413640:0.559169:0.413640:0.559169:0.404091:0.554252:0.404091:0.000000
B:@0.516246:0.411612:0.525436:0.411612:0.525436:0.395143:0.516246:0.395143:0.000000
( ):@0.137759:0.439994:0.183745:0.439994:0.183745:0.409875:0.137759:0.409875:0.000000:0.000000:0.000000
=:@0.124882:0.433248:0.135689:0.433248:0.135689:0.416750:0.124882:0.416750:0.000000
, .  Calcular las medidas de los ángulos interiores del triángu-:@0.163990:0.433248:0.595720:0.434506:0.595720:0.418008:0.163990:0.416750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3 1:@0.154250:0.425684:0.174979:0.426629:0.174979:0.417080:0.154250:0.416135:0.000000:0.000000:0.000000
2:@0.150794:0.435391:0.155711:0.435391:0.155711:0.425843:0.150794:0.425843:0.000000
2:@0.169694:0.435391:0.174611:0.435391:0.174611:0.425843:0.169694:0.425843:0.000000
C:@0.110798:0.433363:0.120836:0.433363:0.120836:0.416895:0.110798:0.416895:0.000000
lo. En la figura 3.27. se muestran los ángulos interiores del triángulo  .:@0.108236:0.457134:0.595695:0.457133:0.595695:0.440636:0.108236:0.440636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.583135:0.457249:0.592941:0.457249:0.592941:0.440780:0.583135:0.440780:0.000000
Cálculo de:@0.108231:0.482075:0.189202:0.482075:0.189202:0.465129:0.108231:0.465129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  . Sean  ,  los vectores que se definen a continuación::@0.189202:0.481612:0.589687:0.481615:0.589687:0.465117:0.189202:0.465115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.193344:0.482162:0.205501:0.482162:0.205501:0.463322:0.193344:0.463322:0.000000
uv:@0.252347:0.481730:0.275061:0.481730:0.275061:0.465262:0.252347:0.465262:0.000000:0.000000
u B A:@0.109720:0.517005:0.171561:0.517005:0.171561:0.500537:0.109720:0.500537:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.122589:0.516890:0.133397:0.516890:0.133397:0.500392:0.122589:0.500392:0.000000
=:@0.174220:0.516890:0.185028:0.516890:0.185028:0.500392:0.174220:0.500392:0.000000
3:@0.209398:0.508055:0.217894:0.508055:0.217894:0.491558:0.209398:0.491558:0.000000
2:@0.203429:0.528246:0.211925:0.528246:0.211925:0.511748:0.203429:0.511748:0.000000
,0:@0.222903:0.516890:0.235541:0.516890:0.235541:0.500392:0.222903:0.500392:0.000000:0.000000
0,0 =:@0.264680:0.516890:0.306271:0.516890:0.306271:0.500392:0.264680:0.500392:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.257561:0.520560:0.292777:0.520560:0.292777:0.499069:0.257561:0.499069:0.000000:0.000000:0.000000
3:@0.330641:0.508055:0.339137:0.508055:0.339137:0.491558:0.330641:0.491558:0.000000
2:@0.324674:0.528246:0.333170:0.528246:0.333170:0.511748:0.324674:0.511748:0.000000
,0 ,:@0.344149:0.516890:0.369467:0.516890:0.369467:0.500392:0.344149:0.500392:0.000000:0.000000:0.000000:0.000000
v C A:@0.108233:0.567619:0.171645:0.567619:0.171645:0.551150:0.108233:0.551150:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.120693:0.567504:0.131501:0.567504:0.131501:0.551006:0.120693:0.551006:0.000000
=:@0.174304:0.567504:0.185111:0.567504:0.185111:0.551006:0.174304:0.551006:0.000000
3 1:@0.209482:0.558669:0.237340:0.558669:0.237340:0.542171:0.209482:0.542171:0.000000:0.000000:0.000000
2 2:@0.203512:0.578858:0.236704:0.578868:0.236704:0.562371:0.203512:0.562361:0.000000:0.000000:0.000000
,:@0.222987:0.567504:0.225742:0.567504:0.225742:0.551006:0.222987:0.551006:0.000000
0,0 =:@0.267381:0.567504:0.308971:0.567504:0.308971:0.551006:0.267381:0.551006:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.260261:0.571174:0.295478:0.571174:0.295478:0.549683:0.260261:0.549683:0.000000:0.000000:0.000000
3 1:@0.333342:0.558669:0.361203:0.558669:0.361203:0.542171:0.333342:0.542171:0.000000:0.000000:0.000000
2 2:@0.327376:0.578858:0.360568:0.578868:0.360568:0.562371:0.327376:0.562361:0.000000:0.000000:0.000000
,:@0.346851:0.567504:0.349606:0.567504:0.349606:0.551006:0.346851:0.551006:0.000000
.:@0.371298:0.567504:0.374053:0.567504:0.374053:0.551006:0.371298:0.551006:0.000000
u A B uv:@0.109175:0.675349:0.212531:0.673009:0.212531:0.656540:0.109175:0.658880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.122045:0.675233:0.132852:0.675233:0.132852:0.658735:0.122045:0.658735:0.000000
=:@0.173681:0.675233:0.184489:0.675233:0.184489:0.658735:0.173681:0.658735:0.000000
3:@0.220213:0.666393:0.228709:0.666393:0.228709:0.649895:0.220213:0.649895:0.000000
2:@0.214244:0.686589:0.222740:0.686589:0.222740:0.670091:0.214244:0.670091:0.000000
,0 ,:@0.233719:0.675233:0.259037:0.675233:0.259037:0.658735:0.233719:0.658735:0.000000:0.000000:0.000000:0.000000
v C B:@0.272219:0.674793:0.332398:0.674793:0.332398:0.658324:0.272219:0.658324:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.284684:0.674677:0.295491:0.674677:0.295491:0.658179:0.284684:0.658179:0.000000
=0,:@0.335153:0.674677:0.367383:0.674677:0.367383:0.658179:0.335153:0.658179:0.000000:0.000000:0.000000
1:@0.370485:0.665843:0.378981:0.665843:0.378981:0.649345:0.370485:0.649345:0.000000
2:@0.369849:0.686042:0.378345:0.686042:0.378345:0.669544:0.369849:0.669544:0.000000
.:@0.389067:0.674677:0.391822:0.674677:0.391822:0.658179:0.389067:0.658179:0.000000
Entonces, :@0.108233:0.620065:0.180380:0.620065:0.180380:0.603567:0.108233:0.603567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.194359:0.620701:0.199175:0.620701:0.199175:0.604420:0.194359:0.604420:0.000000
uv:@0.182530:0.620181:0.208056:0.620181:0.208056:0.603712:0.182530:0.603712:0.000000:0.000000
= ,  :@0.212892:0.620065:0.251541:0.620065:0.251541:0.603567:0.212892:0.603567:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.228131:0.610753:0.236627:0.610753:0.236627:0.594256:0.228131:0.594256:0.000000
4:@0.228125:0.631026:0.236621:0.631026:0.236621:0.614528:0.228125:0.614528:0.000000
u:@0.259333:0.620181:0.268542:0.620181:0.268542:0.603712:0.259333:0.603712:0.000000
=:@0.278020:0.620065:0.288828:0.620065:0.288828:0.603567:0.278020:0.603567:0.000000
3:@0.305878:0.610753:0.314374:0.610753:0.314374:0.594256:0.305878:0.594256:0.000000
2:@0.299904:0.631026:0.308400:0.631026:0.308400:0.614528:0.299904:0.614528:0.000000
,  :@0.319484:0.620065:0.329386:0.620065:0.329386:0.603567:0.319484:0.603567:0.000000:0.000000:0.000000
v:@0.342053:0.620181:0.349836:0.620181:0.349836:0.603712:0.342053:0.603712:0.000000
=1.  Luego,  :@0.360490:0.620065:0.446411:0.620065:0.446411:0.603567:0.360490:0.603567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.137120:0.662569:0.149276:0.662569:0.154049:0.646289:0.141892:0.646289:0.000000
α:@0.334319:0.662569:0.346476:0.662569:0.351248:0.646289:0.339092:0.646289:0.000000
π:@0.367204:0.653257:0.377781:0.653257:0.382553:0.636976:0.371977:0.636976:0.000000
=:@0.161579:0.662569:0.172156:0.662569:0.172156:0.646289:0.161579:0.646289:0.000000
⋅:@0.196546:0.653258:0.201362:0.653258:0.201362:0.636977:0.196546:0.636977:0.000000
=:@0.224981:0.662569:0.235558:0.662569:0.235558:0.646289:0.224981:0.646289:0.000000
=:@0.271372:0.662569:0.281949:0.662569:0.281949:0.646289:0.271372:0.646289:0.000000
=:@0.353288:0.662569:0.363865:0.662569:0.363865:0.646289:0.353288:0.646289:0.000000
cos( ):@0.110796:0.661933:0.158266:0.661933:0.158266:0.645435:0.110796:0.645435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.249371:0.636587:0.257867:0.636587:0.257867:0.620089:0.249371:0.620089:0.000000
4:@0.249371:0.656468:0.257867:0.656468:0.257867:0.639970:0.249371:0.639970:0.000000
3:@0.255131:0.673876:0.263627:0.673876:0.263627:0.657379:0.255131:0.657379:0.000000
2:@0.249163:0.693758:0.257659:0.693758:0.257659:0.677260:0.249163:0.677260:0.000000
3:@0.299996:0.652620:0.308492:0.652620:0.308492:0.636123:0.299996:0.636123:0.000000
2:@0.294027:0.672894:0.302523:0.672894:0.302523:0.656397:0.294027:0.656397:0.000000
6:@0.370876:0.672894:0.379372:0.672894:0.379372:0.656397:0.370876:0.656397:0.000000
.:@0.384281:0.661933:0.387036:0.661933:0.387036:0.645435:0.384281:0.645435:0.000000
uv:@0.184712:0.652737:0.210238:0.652737:0.210238:0.636268:0.184712:0.636268:0.000000:0.000000
Cálculo de:@0.108229:0.711354:0.188970:0.711354:0.188970:0.694408:0.108229:0.694408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  . Para el efecto, se definen los vectores  , , como sigue::@0.188970:0.710891:0.595779:0.710890:0.595779:0.694392:0.188970:0.694394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
β:@0.192880:0.711441:0.203457:0.711441:0.203457:0.692601:0.192880:0.692601:0.000000
uv:@0.476808:0.711006:0.499521:0.711006:0.499521:0.694537:0.476808:0.694537:0.000000:0.000000
u B A:@0.109720:0.588311:0.171542:0.588311:0.171542:0.571842:0.109720:0.571842:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.122589:0.588195:0.133397:0.588195:0.133397:0.571697:0.122589:0.571697:0.000000
=:@0.174201:0.588195:0.185009:0.588195:0.185009:0.571697:0.174201:0.571697:0.000000
3:@0.209379:0.579361:0.217875:0.579361:0.217875:0.562863:0.209379:0.562863:0.000000
2:@0.203407:0.599560:0.211903:0.599560:0.211903:0.583062:0.203407:0.583062:0.000000
,0:@0.222884:0.588209:0.235522:0.588209:0.235522:0.571712:0.222884:0.571712:0.000000:0.000000
0,0 =:@0.264680:0.588195:0.306271:0.588195:0.306271:0.571697:0.264680:0.571697:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.257561:0.591864:0.292777:0.591864:0.292777:0.570373:0.257561:0.570373:0.000000:0.000000:0.000000
3:@0.330641:0.579361:0.339137:0.579361:0.339137:0.562863:0.330641:0.562863:0.000000
2:@0.324674:0.599550:0.333170:0.599550:0.333170:0.583052:0.324674:0.583052:0.000000
,0 ,:@0.344149:0.588195:0.369467:0.588195:0.369467:0.571697:0.344149:0.571697:0.000000:0.000000:0.000000:0.000000
v C A:@0.108233:0.638925:0.171645:0.638925:0.171645:0.622456:0.108233:0.622456:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.120698:0.638809:0.131505:0.638809:0.131505:0.622311:0.120698:0.622311:0.000000
=:@0.174304:0.638809:0.185111:0.638809:0.185111:0.622311:0.174304:0.622311:0.000000
3 1:@0.209482:0.629974:0.237340:0.629974:0.237340:0.613477:0.209482:0.613477:0.000000:0.000000:0.000000
2 2:@0.203512:0.650164:0.236704:0.650174:0.236704:0.633676:0.203512:0.633666:0.000000:0.000000:0.000000
,:@0.222987:0.638809:0.225742:0.638809:0.225742:0.622311:0.222987:0.622311:0.000000
0,0 =:@0.267381:0.638809:0.308971:0.638809:0.308971:0.622311:0.267381:0.622311:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.260261:0.642478:0.295478:0.642478:0.295478:0.620987:0.260261:0.620987:0.000000:0.000000:0.000000
3 1:@0.333342:0.629974:0.361203:0.629974:0.361203:0.613477:0.333342:0.613477:0.000000:0.000000:0.000000
2 2:@0.327376:0.650164:0.360568:0.650174:0.360568:0.633676:0.327376:0.633666:0.000000:0.000000:0.000000
,:@0.346851:0.638809:0.349606:0.638809:0.349606:0.622311:0.346851:0.622311:0.000000
.:@0.371298:0.638809:0.374053:0.638809:0.374053:0.622311:0.371298:0.622311:0.000000
u A B:@0.109175:0.746654:0.170926:0.746654:0.170926:0.730185:0.109175:0.730185:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.122045:0.746538:0.132852:0.746538:0.132852:0.730041:0.122045:0.730041:0.000000
=:@0.173681:0.746538:0.184489:0.746538:0.184489:0.730041:0.173681:0.730041:0.000000
3:@0.220213:0.737698:0.228709:0.737698:0.228709:0.721200:0.220213:0.721200:0.000000
2:@0.214244:0.757894:0.222740:0.757894:0.222740:0.741396:0.214244:0.741396:0.000000
,0 ,:@0.233719:0.746538:0.259037:0.746538:0.259037:0.730041:0.233719:0.730041:0.000000:0.000000:0.000000:0.000000
v C B:@0.272219:0.746098:0.332398:0.746098:0.332398:0.729629:0.272219:0.729629:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.284684:0.745982:0.295491:0.745982:0.295491:0.729485:0.284684:0.729485:0.000000
=0,:@0.335153:0.745982:0.367383:0.745982:0.367383:0.729485:0.335153:0.729485:0.000000:0.000000:0.000000
1:@0.370485:0.737148:0.378981:0.737148:0.378981:0.720650:0.370485:0.720650:0.000000
2:@0.369849:0.757347:0.378345:0.757347:0.378345:0.740850:0.369849:0.740850:0.000000
.:@0.389067:0.745982:0.391822:0.745982:0.391822:0.729485:0.389067:0.729485:0.000000
Calculamos sus longitudes y el producto, y obtenemos::@0.108233:0.786933:0.498487:0.786933:0.498487:0.770435:0.108233:0.770435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.116033:0.823471:0.125242:0.823471:0.125242:0.807002:0.116033:0.807002:0.000000
=:@0.134721:0.823355:0.145529:0.823355:0.145529:0.806858:0.134721:0.806858:0.000000
3:@0.162578:0.814044:0.171074:0.814044:0.171074:0.797546:0.162578:0.797546:0.000000
2:@0.156606:0.834318:0.165102:0.834318:0.165102:0.817820:0.156606:0.817820:0.000000
,  :@0.176186:0.823355:0.186088:0.824613:0.186088:0.808116:0.176186:0.806858:0.000000:0.000000:0.000000
=:@0.217288:0.823992:0.227864:0.823992:0.227864:0.807711:0.217288:0.807711:0.000000
v:@0.198601:0.823471:0.206384:0.823471:0.206384:0.807002:0.198601:0.807002:0.000000
1:@0.233509:0.814044:0.242005:0.814044:0.242005:0.797546:0.233509:0.797546:0.000000
2:@0.232888:0.834318:0.241384:0.834318:0.241384:0.817820:0.232888:0.817820:0.000000
,  :@0.245400:0.823355:0.255553:0.824613:0.255553:0.808116:0.245400:0.806858:0.000000:0.000000:0.000000
uv:@0.257708:0.823471:0.282830:0.823471:0.282830:0.807002:0.257708:0.807002:0.000000:0.000000
=0.  :@0.287800:0.823355:0.320013:0.824613:0.320013:0.808115:0.287800:0.806858:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.269325:0.823992:0.274141:0.823992:0.274141:0.807711:0.269325:0.807711:0.000000
Por lo tanto,  ,  son ortogonales y, en consecuencia, :@0.108230:0.856220:0.491363:0.856220:0.491363:0.839722:0.108230:0.839722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
uv:@0.201855:0.856336:0.224569:0.856336:0.224569:0.839867:0.201855:0.839867:0.000000:0.000000
ββ:@0.140237:0.892154:0.156064:0.892154:0.156064:0.875483:0.140237:0.875483:0.000000:0.000000
⋅⋅:@0.194863:0.882619:0.204792:0.882619:0.204792:0.865948:0.194863:0.865948:0.000000:0.000000
→β→β:@0.249543:0.892154:0.287569:0.892154:0.287569:0.875483:0.249543:0.875483:0.000000:0.000000:0.000000:0.000000
π π:@0.301703:0.882619:0.317529:0.882619:0.317529:0.865947:0.301703:0.865948:0.000000:0.000000:0.000000
uvuv:@0.182748:0.882086:0.213884:0.882086:0.213884:0.865222:0.182748:0.865222:0.000000:0.000000:0.000000:0.000000
uvuv:@0.180380:0.902844:0.216232:0.902844:0.216232:0.885980:0.180380:0.885980:0.000000:0.000000:0.000000:0.000000
cos( )=)=:@0.110860:0.891503:0.175908:0.891503:0.175908:0.874609:0.110860:0.874609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=0 =0:@0.223543:0.891503:0.251288:0.891503:0.251288:0.874609:0.223543:0.874609:0.000000:0.000000:0.000000:0.000000:0.000000
= ..:@0.285725:0.891503:0.323631:0.891503:0.323631:0.874609:0.285725:0.874609:0.000000:0.000000:0.000000:0.000000
22:@0.302296:0.902726:0.315996:0.902726:0.315996:0.885832:0.302296:0.885832:0.000000:0.000000
   :@0.248318:0.890841:0.275617:0.890841:0.275617:0.874343:0.248318:0.874343:0.000000:0.000000:0.000000
⇒:@0.252460:0.891391:0.271475:0.891391:0.271475:0.872551:0.252460:0.872551:0.000000
co:@0.115858:0.891503:0.133395:0.891503:0.133395:0.874609:0.115858:0.874609:0.000000:0.000000
s(:@0.133060:0.891503:0.146080:0.891503:0.146080:0.874609:0.133060:0.874609:0.000000:0.000000
=:@0.290725:0.891503:0.301792:0.891503:0.301792:0.874609:0.290725:0.874609:0.000000
Así,  :@0.108233:0.924205:0.141485:0.924205:0.141485:0.907707:0.108233:0.907707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6:@0.292622:0.936424:0.301118:0.936424:0.301118:0.919927:0.292622:0.919927:0.000000
2:@0.323658:0.936424:0.332154:0.936424:0.332154:0.919927:0.323658:0.919927:0.000000
3:@0.356698:0.936424:0.365194:0.936424:0.365194:0.919927:0.356698:0.919927:0.000000
, .:@0.370839:0.925464:0.371639:0.924204:0.371639:0.907707:0.370839:0.908967:0.000000:0.000000:0.000000
γ:@0.141997:0.926098:0.149915:0.926098:0.154687:0.909818:0.146769:0.909818:0.000000
π αβ π:@0.171376:0.926098:0.269783:0.926098:0.274556:0.909818:0.176149:0.909818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
π:@0.288946:0.916787:0.299523:0.916787:0.304295:0.900506:0.293718:0.900506:0.000000
π:@0.320194:0.916787:0.330771:0.916787:0.335543:0.900506:0.324967:0.900506:0.000000
π:@0.353025:0.916786:0.363602:0.916786:0.368374:0.900506:0.357797:0.900506:0.000000
= −−= −:@0.158969:0.926098:0.286390:0.926098:0.286390:0.909818:0.158969:0.909818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.307061:0.926098:0.317638:0.926098:0.317638:0.909818:0.307061:0.909818:0.000000
=:@0.339100:0.926098:0.349676:0.926098:0.349676:0.909818:0.339100:0.909818:0.000000
–1:@0.645658:0.220494:0.660703:0.220494:0.660703:0.207570:0.645658:0.207570:0.000000:0.000000
1:@0.791057:0.220494:0.797954:0.220494:0.797954:0.207570:0.791057:0.207570:0.000000
x:@0.836385:0.215027:0.842388:0.215027:0.842388:0.202047:0.836385:0.202047:0.000000
1:@0.705123:0.173528:0.712020:0.173528:0.712020:0.160604:0.705123:0.160604:0.000000
0:@0.702069:0.214904:0.708966:0.214904:0.708966:0.201980:0.702069:0.201980:0.000000
y:@0.711379:0.102135:0.717576:0.102135:0.717576:0.089155:0.711379:0.089155:0.000000
2:@0.705123:0.138323:0.712020:0.138323:0.712020:0.125400:0.705123:0.125400:0.000000
B:@0.790379:0.143054:0.798125:0.143054:0.798125:0.130053:0.790379:0.130053:0.000000
A:@0.666847:0.155162:0.676291:0.155162:0.676291:0.142160:0.666847:0.142160:0.000000
S:@0.823513:0.119647:0.830083:0.119647:0.830083:0.106645:0.823513:0.106645:0.000000
p:@0.787313:0.254158:0.798794:0.254158:0.798794:0.244134:0.787313:0.244134:0.000000
 Figura 3.26.:@0.798794:0.254866:0.856154:0.254866:0.856154:0.243390:0.798794:0.243390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.674724:0.672149:0.682551:0.672149:0.682551:0.661666:0.674724:0.661666:0.000000
β:@0.796987:0.669394:0.803798:0.669394:0.803798:0.658910:0.796987:0.658910:0.000000
γ:@0.797099:0.605591:0.802197:0.605591:0.802197:0.595108:0.797099:0.595108:0.000000
0:@0.645104:0.682762:0.650599:0.682762:0.650599:0.671953:0.645104:0.671953:0.000000
C:@0.812611:0.587461:0.819198:0.587461:0.819198:0.576652:0.812611:0.576652:0.000000
A:@0.641249:0.671290:0.648692:0.671290:0.648692:0.660481:0.641249:0.660481:0.000000
x:@0.839691:0.685078:0.844690:0.685078:0.844690:0.674269:0.839691:0.674269:0.000000
y:@0.642042:0.564623:0.647203:0.564623:0.647203:0.553814:0.642042:0.553814:0.000000
v:@0.729634:0.625074:0.734844:0.625074:0.734844:0.614265:0.729634:0.614265:0.000000
u:@0.724430:0.688275:0.730558:0.688275:0.730558:0.677466:0.724430:0.677466:0.000000
√3:@0.799589:0.685084:0.811411:0.685084:0.811411:0.674275:0.799589:0.674275:0.000000:0.000000
2:@0.802753:0.695083:0.808248:0.695083:0.808248:0.684274:0.802753:0.684274:0.000000
, 0:@0.813607:0.688278:0.824040:0.688278:0.824040:0.677468:0.813607:0.677468:0.000000:0.000000:0.000000
B =:@0.776938:0.690093:0.792916:0.690093:0.792916:0.679284:0.776938:0.679284:0.000000:0.000000:0.000000
p:@0.787313:0.717460:0.798794:0.717460:0.798794:0.707435:0.787313:0.707435:0.000000
 :@0.798794:0.718168:0.801675:0.718168:0.801675:0.706691:0.798794:0.706691:0.000000
Figura 3.27.:@0.801675:0.718168:0.856154:0.718168:0.856154:0.706691:0.801675:0.706691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.684804:0.292026:0.782426:0.292026:0.782426:0.276554:0.684804:0.276554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684804:0.304594:0.768866:0.304594:0.768866:0.289122:0.684804:0.289122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El teorema de Pitágoras :@0.685042:0.329068:0.840940:0.329068:0.840940:0.314005:0.685042:0.314005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
enuncia que, en todo triángulo :@0.638498:0.344910:0.842611:0.344910:0.842611:0.329847:0.638498:0.329847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectángulo, la hipotenusa al :@0.638498:0.360752:0.820606:0.360752:0.820606:0.345689:0.638498:0.345689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadrado es igual a la suma de :@0.638498:0.376594:0.839443:0.376594:0.839443:0.361531:0.638498:0.361531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los cuadrados de los catetos. :@0.638498:0.392436:0.826956:0.392436:0.826956:0.377373:0.638498:0.377373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Este resultado es extendido al :@0.638498:0.408278:0.834342:0.408278:0.834342:0.393215:0.638498:0.393215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
espacio euclídeo  .:@0.638498:0.424120:0.769654:0.424120:0.769654:0.409057:0.638498:0.409057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.749914:0.423235:0.762614:0.423235:0.762614:0.410958:0.749914:0.410958:0.000000
2:@0.762617:0.418320:0.767139:0.418320:0.767139:0.409539:0.762617:0.409539:0.000000
Teorema de Pitágoras:@0.638503:0.445731:0.789703:0.445731:0.789703:0.430258:0.638503:0.430258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.638503:0.469639:0.673014:0.469639:0.673014:0.454576:0.638503:0.454576:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.676560:0.469139:0.703691:0.469139:0.703691:0.453436:0.676560:0.453436:0.000000:0.000000
,:@0.688298:0.469029:0.690924:0.469029:0.690924:0.453298:0.688298:0.453298:0.000000
2:@0.733863:0.461366:0.738552:0.461366:0.738552:0.452261:0.733863:0.452261:0.000000
∈:@0.706609:0.469635:0.719706:0.469635:0.719706:0.454112:0.706609:0.454112:0.000000
.  :@0.738622:0.469639:0.748701:0.469639:0.748701:0.454576:0.738622:0.454576:0.000000:0.000000:0.000000
Entonces, :@0.638500:0.485481:0.704373:0.485481:0.704373:0.470418:0.638500:0.470418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⊥:@0.722595:0.486438:0.735272:0.486438:0.735272:0.470157:0.722595:0.470157:0.000000
A:@0.708089:0.485917:0.719359:0.485917:0.719359:0.469449:0.708089:0.469449:0.000000
B:@0.739086:0.485917:0.748276:0.485917:0.748276:0.469449:0.739086:0.469449:0.000000
 si y solo si :@0.751284:0.485481:0.822697:0.485481:0.822697:0.470418:0.751284:0.470418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.661590:0.506680:0.672166:0.506680:0.672166:0.490400:0.661590:0.490400:0.000000
=:@0.700332:0.506680:0.710909:0.506680:0.710909:0.490400:0.700332:0.490400:0.000000
+:@0.747860:0.506680:0.758436:0.506680:0.758436:0.490400:0.747860:0.490400:0.000000
AB:@0.647873:0.506160:0.684072:0.506160:0.684072:0.489691:0.647873:0.489691:0.000000:0.000000
A:@0.721218:0.506160:0.732489:0.506160:0.732489:0.489691:0.721218:0.489691:0.000000
B:@0.766819:0.506160:0.776009:0.506160:0.776009:0.489691:0.766819:0.489691:0.000000
.:@0.790419:0.506044:0.793174:0.506044:0.793174:0.489546:0.790419:0.489546:0.000000
2:@0.690069:0.495887:0.694986:0.495887:0.694986:0.486339:0.690069:0.486339:0.000000
2:@0.738385:0.495887:0.743303:0.495887:0.743303:0.486339:0.738385:0.486339:0.000000
2:@0.781998:0.495887:0.786915:0.495887:0.786915:0.486339:0.781998:0.486339:0.000000
.:@0.788246:0.505724:0.790762:0.505724:0.790762:0.490660:0.788246:0.490660:0.000000
Competencia :@0.684804:0.763939:0.782426:0.763939:0.782426:0.748467:0.684804:0.748467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684804:0.776507:0.768866:0.776507:0.768866:0.761035:0.684804:0.761035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ley de cosenos:@0.685042:0.801404:0.788436:0.801404:0.788436:0.785932:0.685042:0.785932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.638498:0.825312:0.673010:0.825312:0.673010:0.810249:0.638498:0.810249:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.676560:0.824812:0.703691:0.824812:0.703691:0.809109:0.676560:0.809109:0.000000:0.000000
,:@0.688298:0.824702:0.690924:0.824702:0.690924:0.808971:0.688298:0.808971:0.000000
2:@0.733863:0.817040:0.738552:0.817040:0.738552:0.807935:0.733863:0.807935:0.000000
∈:@0.706609:0.825308:0.719706:0.825308:0.719706:0.809785:0.706609:0.809785:0.000000
 no nulos y :@0.741700:0.825313:0.817038:0.825313:0.817038:0.810250:0.741700:0.810250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[ ]:@0.666460:0.847189:0.704971:0.847189:0.704971:0.824070:0.666460:0.824070:0.000000:0.000000:0.000000
θ∈:@0.641068:0.843998:0.667693:0.843998:0.667693:0.827717:0.641068:0.827717:0.000000:0.000000
π:@0.687035:0.843998:0.697612:0.843998:0.697612:0.827717:0.687035:0.827717:0.000000
0,:@0.673992:0.843362:0.685166:0.843362:0.685166:0.826864:0.673992:0.826864:0.000000:0.000000
 el ángulo que for-:@0.707188:0.843041:0.824549:0.843041:0.824549:0.827978:0.707188:0.827978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
man los vectores :@0.638499:0.862025:0.751707:0.862025:0.751707:0.846962:0.638499:0.846962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.755428:0.862463:0.791955:0.862463:0.791955:0.845994:0.755428:0.845994:0.000000:0.000000
y:@0.770715:0.862347:0.778537:0.862347:0.778537:0.845849:0.770715:0.845849:0.000000
.  :@0.792996:0.862026:0.803075:0.862026:0.803075:0.846963:0.792996:0.846963:0.000000:0.000000:0.000000
Como :@0.638503:0.881010:0.683375:0.881010:0.683375:0.865947:0.638503:0.865947:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.699971:0.881968:0.704788:0.881968:0.704788:0.865688:0.699971:0.865688:0.000000
θ:@0.804370:0.881968:0.814407:0.881968:0.814407:0.865688:0.804370:0.865688:0.000000
AB:@0.687092:0.881448:0.715239:0.881448:0.715239:0.864979:0.687092:0.864979:0.000000:0.000000
AB:@0.739243:0.881448:0.771994:0.881448:0.771994:0.864979:0.739243:0.864979:0.000000:0.000000
=:@0.719131:0.881332:0.729939:0.881332:0.729939:0.864834:0.719131:0.864834:0.000000
cos ,:@0.779701:0.881332:0.818214:0.881332:0.818214:0.864834:0.779701:0.864834:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.822420:0.881012:0.829983:0.881012:0.829983:0.865948:0.822420:0.865948:0.000000:0.000000
resulta que :@0.638498:0.896854:0.713836:0.896854:0.713836:0.881790:0.638498:0.881790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.655291:0.915719:0.663770:0.915719:0.663770:0.902668:0.655291:0.902668:0.000000
+:@0.724278:0.915719:0.732757:0.915719:0.732757:0.902668:0.724278:0.902668:0.000000
−:@0.761759:0.915719:0.770238:0.915719:0.770238:0.902668:0.761759:0.902668:0.000000
θ:@0.837974:0.915719:0.846020:0.915719:0.846020:0.902668:0.837974:0.902668:0.000000
BA:@0.645092:0.915302:0.675902:0.915302:0.675902:0.902100:0.645092:0.902100:0.000000:0.000000
B:@0.703716:0.915302:0.711083:0.915302:0.711083:0.902100:0.703716:0.902100:0.000000
A:@0.740395:0.915302:0.749430:0.915302:0.749430:0.902100:0.740395:0.902100:0.000000
AB:@0.785769:0.915302:0.812023:0.915302:0.812023:0.902100:0.785769:0.902100:0.000000:0.000000
=:@0.688528:0.915209:0.697192:0.915209:0.697192:0.901984:0.688528:0.901984:0.000000
2:@0.772418:0.915209:0.779229:0.915209:0.779229:0.901984:0.772418:0.901984:0.000000
cos.:@0.818203:0.915209:0.848493:0.915209:0.848493:0.901984:0.818203:0.901984:0.000000:0.000000:0.000000:0.000000
2:@0.680637:0.905870:0.684579:0.905870:0.684579:0.898215:0.680637:0.898215:0.000000
2:@0.716688:0.905870:0.720630:0.905870:0.720630:0.898215:0.716688:0.898215:0.000000
2:@0.754160:0.905870:0.758102:0.905870:0.758102:0.898215:0.754160:0.898215:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000