213:@0.918240:0.966765:0.943652:0.966765:0.943652:0.950778:0.918240:0.950778:0.000000:0.000000:0.000000
 :@0.546479:0.952465:0.549361:0.952465:0.549361:0.940988:0.546479:0.940988:0.000000
Figura 6.7.:@0.549361:0.952465:0.597929:0.952465:0.597929:0.940988:0.549361:0.940988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.145514:0.935638:0.152532:0.935638:0.152532:0.922010:0.145514:0.922010:0.000000
z:@0.142156:0.776981:0.147646:0.776981:0.147646:0.763377:0.142156:0.763377:0.000000
x:@0.577648:0.937979:0.583823:0.937979:0.583823:0.924375:0.577648:0.924375:0.000000
y:@0.553107:0.766888:0.559457:0.766888:0.559457:0.753284:0.553107:0.753284:0.000000
c + z:@0.126646:0.834829:0.149603:0.834829:0.149603:0.823372:0.126646:0.823372:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.144604:0.874570:0.149603:0.874570:0.149603:0.863113:0.144604:0.863113:0.000000
z:@0.144979:0.889537:0.149603:0.889537:0.149603:0.878080:0.144979:0.878080:0.000000
y:@0.210381:0.897060:0.215728:0.897060:0.215728:0.885604:0.210381:0.885604:0.000000
b:@0.226530:0.889215:0.232976:0.889215:0.232976:0.877758:0.226530:0.877758:0.000000
b + y:@0.247196:0.873302:0.268304:0.873302:0.268304:0.861846:0.247196:0.861846:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.214616:0.937465:0.220861:0.937465:0.220861:0.926008:0.214616:0.926008:0.000000
x:@0.286370:0.937465:0.291570:0.937465:0.291570:0.926008:0.286370:0.926008:0.000000
a + x:@0.369180:0.937465:0.393960:0.937465:0.393960:0.926008:0.369180:0.926008:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.250623:0.857050:0.258231:0.857050:0.258231:0.843445:0.250623:0.843445:0.000000
:@0.253058:0.857360:0.258358:0.857360:0.258358:0.844293:0.253058:0.844293:0.000000
u:@0.424683:0.832050:0.432291:0.832050:0.432291:0.818446:0.424683:0.818446:0.000000
:@0.427118:0.832361:0.432418:0.832361:0.432418:0.819294:0.427118:0.819294:0.000000
v:@0.318277:0.888129:0.324707:0.888129:0.324707:0.874525:0.318277:0.874525:0.000000
:@0.319534:0.888440:0.324834:0.888440:0.324834:0.875373:0.319534:0.875373:0.000000
v:@0.367502:0.803396:0.373931:0.803396:0.373931:0.789791:0.367502:0.789791:0.000000
:@0.368759:0.803706:0.374058:0.803706:0.374058:0.790639:0.368759:0.790639:0.000000
u v:@0.325152:0.832433:0.355088:0.832433:0.355088:0.818828:0.325152:0.818828:0.000000:0.000000:0.000000
:@0.327587:0.832743:0.332887:0.832743:0.332887:0.819676:0.327587:0.819676:0.000000
 +   :@0.332887:0.832337:0.359035:0.832337:0.359035:0.818709:0.332887:0.818709:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.350314:0.832743:0.355613:0.832743:0.355613:0.819676:0.350314:0.819676:0.000000
p:@0.793223:0.617777:0.804704:0.617777:0.804704:0.607753:0.793223:0.607753:0.000000
 :@0.804704:0.618485:0.807585:0.618485:0.807585:0.607009:0.804704:0.607009:0.000000
Figura 6.6.:@0.807585:0.618485:0.856154:0.618485:0.856154:0.607009:0.807585:0.607009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.701132:0.494968:0.706131:0.494968:0.706131:0.483511:0.701132:0.483511:0.000000
a:@0.660216:0.571995:0.666461:0.571995:0.666461:0.560539:0.660216:0.560539:0.000000
b:@0.809071:0.554614:0.815518:0.554614:0.815518:0.543158:0.809071:0.543158:0.000000
A:@0.780701:0.517791:0.790011:0.517791:0.790011:0.504186:0.780701:0.504186:0.000000
0:@0.699973:0.540161:0.706991:0.540161:0.706991:0.526533:0.699973:0.526533:0.000000
z:@0.697204:0.473523:0.703044:0.473523:0.703044:0.459895:0.697204:0.459895:0.000000
y:@0.837620:0.555247:0.844081:0.555247:0.844081:0.541618:0.837620:0.541618:0.000000
x:@0.650478:0.604087:0.657083:0.604087:0.657083:0.590459:0.650478:0.590459:0.000000
OA:@0.727938:0.527879:0.747605:0.527879:0.747605:0.513880:0.727938:0.513880:0.000000:0.000000
La :@0.108231:0.200514:0.128594:0.200514:0.128594:0.184016:0.108231:0.184016:0.000000:0.000000:0.000000
norma o longitud:@0.132833:0.200976:0.275933:0.200976:0.275933:0.184031:0.132833:0.184031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 del vector u, se escribe como |u| o ||u|| :@0.275916:0.200514:0.599954:0.200514:0.599954:0.184016:0.275916:0.184016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.595777:0.200514:0.599919:0.200514:0.599919:0.184016:0.595777:0.184016:0.000000
y se define por:@0.108250:0.217864:0.213053:0.217864:0.213053:0.201367:0.108250:0.201367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entonces: la distancia  d(u,v) = || u – v || = :@0.108250:0.287268:0.412025:0.287268:0.412025:0.270770:0.108250:0.270770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos:@0.108250:0.305081:0.178046:0.305081:0.178046:0.288135:0.108250:0.288135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.178046:0.304618:0.180801:0.304618:0.180801:0.288121:0.178046:0.288121:0.000000
1.:@0.108250:0.322186:0.120522:0.322186:0.120522:0.305471:0.108250:0.305471:0.000000:0.000000
 :@0.120522:0.322432:0.124549:0.322432:0.124549:0.305486:0.120522:0.305486:0.000000
Si  u = (4, 5, 2) entonces la norma o longitud de u es:  :@0.124549:0.321969:0.504436:0.321969:0.504436:0.305471:0.124549:0.305471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.108250:0.395146:0.120522:0.395146:0.120522:0.378431:0.108250:0.378431:0.000000:0.000000
  :@0.120522:0.395392:0.128575:0.395392:0.128575:0.378446:0.120522:0.378446:0.000000:0.000000
Sean  u = (1, 5, 2)  y  v = (5, - 2, - 5);  la distancia entre u y v es::@0.128575:0.394929:0.575394:0.394929:0.575394:0.378431:0.128575:0.378431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interpretación geométrica de las operaciones en :@0.108233:0.454441:0.499067:0.454441:0.499067:0.436759:0.108233:0.436759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.499067:0.452948:0.513581:0.452948:0.513581:0.438916:0.499067:0.438916:0.000000
3:@0.513577:0.447612:0.519285:0.447612:0.519285:0.437302:0.513577:0.437302:0.000000
Consideremos el sistema de coordenadas ortogonales :@0.108233:0.471149:0.496480:0.471149:0.496480:0.454651:0.108233:0.454651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xyz:@0.497154:0.471265:0.519153:0.471265:0.519153:0.454796:0.497154:0.454796:0.000000:0.000000:0.000000
; y denote-:@0.519153:0.471149:0.595810:0.471149:0.595810:0.454651:0.519153:0.454651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mos con O el punto de intersección de los tres ejes. Sea::@0.108233:0.488500:0.504824:0.488500:0.504824:0.472002:0.108233:0.472002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.108233:0.505966:0.119503:0.505966:0.119503:0.489497:0.108233:0.489497:0.000000
 = ( ,  ,  )   :@0.119503:0.505851:0.221147:0.505851:0.221147:0.489353:0.119503:0.489353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.148006:0.505966:0.190688:0.505966:0.190688:0.489497:0.148006:0.489497:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.202494:0.505332:0.217146:0.505332:0.217146:0.491959:0.202494:0.491959:0.000000
R:@0.222719:0.504764:0.236024:0.504764:0.236024:0.491901:0.222719:0.491901:0.000000
3:@0.235876:0.499498:0.240829:0.499498:0.240829:0.489879:0.235876:0.489879:0.000000
. Tal como procedimos en el caso bidimensional, :@0.240828:0.505851:0.599956:0.505851:0.599956:0.489353:0.240828:0.489353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trazamos el vector geométrico :@0.108226:0.523201:0.336151:0.523201:0.336151:0.506704:0.108226:0.506704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
OA:@0.338386:0.523317:0.361523:0.523317:0.361523:0.506848:0.338386:0.506848:0.000000:0.000000
. Se establece una identificación :@0.361525:0.523201:0.599910:0.523201:0.599910:0.506704:0.361525:0.506704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre cada punto       con el respectivo vector geométrico :@0.108226:0.540552:0.548430:0.540552:0.548430:0.524054:0.108226:0.524054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.234449:0.540668:0.245720:0.540668:0.245720:0.524199:0.234449:0.524199:0.000000
:@0.249603:0.540033:0.264256:0.540033:0.264256:0.526660:0.249603:0.526660:0.000000
R:@0.267820:0.539465:0.281124:0.539465:0.281124:0.526603:0.267820:0.526603:0.000000
3:@0.280975:0.534199:0.285929:0.534199:0.285929:0.524581:0.280975:0.524581:0.000000
OA:@0.548141:0.540668:0.571278:0.540668:0.571278:0.524199:0.548141:0.524199:0.000000:0.000000
. En :@0.571305:0.540552:0.599895:0.540552:0.599895:0.524054:0.571305:0.524054:0.000000:0.000000:0.000000:0.000000:0.000000
la Figura 6.6. se muestra este vector :@0.108226:0.557903:0.361351:0.557903:0.361351:0.541405:0.108226:0.541405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
OA:@0.361351:0.558018:0.384488:0.558018:0.384488:0.541550:0.361351:0.541550:0.000000:0.000000
.:@0.384490:0.557903:0.387245:0.557903:0.387245:0.541405:0.384490:0.541405:0.000000
Sean   = ( ,  ,  ),   = ( ,  ,  ) dos elementos de  . De la definición de :@0.108226:0.592604:0.599887:0.592604:0.599887:0.576107:0.108226:0.576107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.145774:0.592720:0.154983:0.592720:0.154983:0.576251:0.145774:0.576251:0.000000
:@0.148722:0.593096:0.155137:0.593096:0.155137:0.577278:0.148722:0.577278:0.000000
a b c v:@0.179681:0.592720:0.238806:0.592720:0.238806:0.576251:0.179681:0.576251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.233027:0.593096:0.239442:0.593096:0.239442:0.577278:0.233027:0.577278:0.000000
x y z:@0.263986:0.592720:0.299107:0.592720:0.299107:0.576251:0.263986:0.576251:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.437903:0.591517:0.451208:0.591517:0.451208:0.578655:0.437903:0.578655:0.000000
3:@0.451061:0.586251:0.456014:0.586251:0.456014:0.576633:0.451061:0.576633:0.000000
suma de elementos de   se tiene::@0.108238:0.609955:0.351936:0.609955:0.351936:0.593457:0.108238:0.593457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.272660:0.608868:0.285964:0.608868:0.285964:0.596006:0.272660:0.596006:0.000000
3:@0.285817:0.603602:0.290770:0.603602:0.290770:0.593984:0.285817:0.593984:0.000000
u v:@0.189127:0.634550:0.225365:0.634550:0.225365:0.618081:0.189127:0.618081:0.000000:0.000000:0.000000
:@0.192075:0.634926:0.198490:0.634926:0.198490:0.619108:0.192075:0.619108:0.000000
 +   = ( ,  ,  ) + ( ,  ,  ) = (  +  ,   +  ,   +  ).:@0.198490:0.634434:0.514883:0.634434:0.514883:0.617936:0.198490:0.617936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.219585:0.634926:0.226001:0.634926:0.226001:0.619108:0.219585:0.619108:0.000000
a b c:@0.251046:0.634550:0.290270:0.634550:0.290270:0.618081:0.251046:0.618081:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.321267:0.634550:0.356870:0.634550:0.356870:0.618081:0.321267:0.618081:0.000000:0.000000:0.000000:0.000000:0.000000
a x b y c z:@0.387867:0.634550:0.506175:0.634550:0.506175:0.618081:0.387867:0.618081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108232:0.651785:0.112374:0.651785:0.112374:0.635287:0.108232:0.635287:0.000000
Interpretemos geométricamente este resultado. Primeramente, los :@0.108232:0.669136:0.599891:0.669136:0.599891:0.652638:0.108232:0.652638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puntos ( ,  ,  ), ( ,  ,  )     se identifican con los vectores geométri-:@0.108232:0.686486:0.595776:0.686486:0.595776:0.669988:0.108232:0.669989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c x y z:@0.168552:0.686602:0.260640:0.686602:0.260640:0.670133:0.168552:0.670133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.270420:0.685967:0.285072:0.685967:0.285072:0.672594:0.270420:0.672594:0.000000
R:@0.288609:0.685399:0.301914:0.685399:0.301914:0.672537:0.288609:0.672537:0.000000
3:@0.301767:0.680134:0.306720:0.680134:0.306720:0.670516:0.301767:0.670516:0.000000
cos notados  ,   respectivamente. Representamos el vector geomé-:@0.108231:0.703836:0.595776:0.703836:0.595776:0.687339:0.108231:0.687339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.201320:0.703952:0.226500:0.703952:0.226500:0.687483:0.201320:0.687483:0.000000:0.000000:0.000000
 :@0.204268:0.704328:0.227136:0.704328:0.227136:0.688510:0.204268:0.688510:0.000000:0.000000:0.000000
trico   +   que se identifica con el punto (  +  ,   +  ,   +  )    . En :@0.108250:0.721187:0.599914:0.721187:0.599914:0.704690:0.108250:0.704690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.145124:0.721303:0.181246:0.721303:0.181246:0.704834:0.145124:0.704834:0.000000:0.000000:0.000000
:@0.148071:0.721679:0.154486:0.721679:0.154486:0.705861:0.148071:0.705861:0.000000
:@0.175447:0.721679:0.181862:0.721679:0.181862:0.705861:0.175447:0.705861:0.000000
a x b y c z:@0.406761:0.721303:0.524533:0.721303:0.524533:0.704834:0.406761:0.704834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.534548:0.720669:0.549201:0.720669:0.549201:0.707295:0.534548:0.707295:0.000000
R:@0.552984:0.720100:0.566289:0.720100:0.566289:0.707238:0.552984:0.707238:0.000000
3:@0.566141:0.714835:0.571095:0.714835:0.571095:0.705217:0.566141:0.705217:0.000000
la Figura 6.7. se muestra esta representación.:@0.108226:0.738538:0.419955:0.738538:0.419955:0.722040:0.108226:0.722040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d u v:@0.127952:0.423941:0.162504:0.423941:0.162504:0.408188:0.127952:0.408188:0.000000:0.000000:0.000000:0.000000:0.000000
( , ):@0.137111:0.423830:0.168346:0.423830:0.168346:0.408049:0.137111:0.408049:0.000000:0.000000:0.000000:0.000000:0.000000
= − =:@0.170981:0.424438:0.236856:0.424438:0.236856:0.408865:0.170981:0.408865:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.188579:0.423941:0.218119:0.423941:0.218119:0.408188:0.188579:0.408188:0.000000:0.000000:0.000000
(1 5) (5 2):@0.251820:0.423830:0.347293:0.423830:0.347293:0.408049:0.251820:0.408049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.264756:0.424438:0.274872:0.424438:0.274872:0.408865:0.264756:0.408865:0.000000
2:@0.291236:0.416138:0.295946:0.416138:0.295946:0.406993:0.291236:0.406993:0.000000
+ +:@0.297465:0.424438:0.331924:0.424438:0.331924:0.408865:0.297465:0.408865:0.000000:0.000000:0.000000
2:@0.347618:0.416138:0.352328:0.416138:0.352328:0.406993:0.347618:0.406993:0.000000
+ +:@0.355733:0.424438:0.392865:0.424438:0.392865:0.408865:0.355733:0.408865:0.000000:0.000000:0.000000
(2 5):@0.367564:0.423830:0.407441:0.423830:0.407441:0.408049:0.367564:0.408049:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.407769:0.416138:0.412479:0.416138:0.412479:0.406993:0.407769:0.406993:0.000000
=:@0.418501:0.424438:0.428618:0.424438:0.428618:0.408865:0.418501:0.408865:0.000000
16 49 49:@0.442788:0.423830:0.519153:0.423830:0.519153:0.408049:0.442788:0.408049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.460682:0.424438:0.470798:0.424438:0.470798:0.408865:0.460682:0.408865:0.000000
+:@0.490774:0.424438:0.500891:0.424438:0.500891:0.408865:0.490774:0.408865:0.000000
=:@0.523518:0.424438:0.533635:0.424438:0.533635:0.408865:0.523518:0.408865:0.000000
114:@0.547806:0.423830:0.572038:0.423830:0.572038:0.408049:0.547806:0.408049:0.000000:0.000000:0.000000
u:@0.238908:0.236221:0.250626:0.236221:0.250626:0.215266:0.238908:0.215266:0.000000
=:@0.261333:0.236883:0.274791:0.236883:0.274791:0.216167:0.261333:0.216167:0.000000
u:@0.294133:0.236221:0.305850:0.236221:0.305850:0.215266:0.294133:0.215266:0.000000
1:@0.304928:0.238910:0.311193:0.238910:0.311193:0.226745:0.304928:0.226745:0.000000
2:@0.306249:0.225849:0.312514:0.225849:0.312514:0.213683:0.306249:0.213683:0.000000
+:@0.317047:0.236883:0.330505:0.236883:0.330505:0.216167:0.317047:0.216167:0.000000
u:@0.332221:0.236221:0.343938:0.236221:0.343938:0.215266:0.332221:0.215266:0.000000
2:@0.343649:0.238910:0.349915:0.238910:0.349915:0.226745:0.343649:0.226745:0.000000
2:@0.344346:0.225849:0.350611:0.225849:0.350611:0.213683:0.344346:0.213683:0.000000
+:@0.355140:0.236883:0.368598:0.236883:0.368598:0.216167:0.355140:0.216167:0.000000
u:@0.370314:0.236221:0.382032:0.236221:0.382032:0.215266:0.370314:0.215266:0.000000
3:@0.381743:0.238910:0.388008:0.238910:0.388008:0.226745:0.381743:0.226745:0.000000
2:@0.382439:0.225849:0.388704:0.225849:0.388704:0.213683:0.382439:0.213683:0.000000
=:@0.396716:0.236883:0.410174:0.236883:0.410174:0.216167:0.396716:0.216167:0.000000
u u:@0.429516:0.236221:0.461571:0.236221:0.461571:0.215266:0.429516:0.215266:0.000000:0.000000:0.000000
⋅:@0.443586:0.235383:0.448043:0.235383:0.448043:0.220317:0.443586:0.220317:0.000000
u:@0.218688:0.359521:0.229569:0.359521:0.229569:0.340062:0.218688:0.340062:0.000000
=:@0.239512:0.360136:0.252009:0.360136:0.252009:0.340899:0.239512:0.340899:0.000000
u u:@0.269969:0.359521:0.300518:0.359521:0.300518:0.340062:0.269969:0.340062:0.000000:0.000000:0.000000
⋅:@0.282648:0.360136:0.288339:0.360136:0.288339:0.340899:0.282648:0.340899:0.000000
=:@0.305539:0.360136:0.318037:0.360136:0.318037:0.340899:0.305539:0.340899:0.000000
4:@0.336976:0.359384:0.347015:0.359384:0.347015:0.339891:0.336976:0.339891:0.000000
2:@0.347704:0.349884:0.353521:0.349884:0.353521:0.338587:0.347704:0.338587:0.000000
+ +:@0.357728:0.360136:0.404628:0.360136:0.404628:0.340899:0.357728:0.340899:0.000000:0.000000:0.000000
5:@0.371819:0.359384:0.381857:0.359384:0.381857:0.339891:0.371819:0.339891:0.000000
2:@0.382108:0.349884:0.387926:0.349884:0.387926:0.338587:0.382108:0.338587:0.000000
2:@0.406745:0.359384:0.416784:0.359384:0.416784:0.339891:0.406745:0.339891:0.000000
2:@0.417482:0.349884:0.423300:0.349884:0.423300:0.338587:0.417482:0.338587:0.000000
=:@0.430738:0.360136:0.443236:0.360136:0.443236:0.340899:0.430738:0.340899:0.000000
45:@0.462175:0.359384:0.482161:0.359384:0.482161:0.339891:0.462175:0.339891:0.000000:0.000000
(:@0.431774:0.271622:0.438870:0.271622:0.438870:0.251957:0.431774:0.251957:0.000000
u v u v:@0.437905:0.271759:0.534353:0.271759:0.534353:0.252129:0.437905:0.252129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.451224:0.272380:0.463831:0.272380:0.463831:0.252974:0.451224:0.252974:0.000000
) (:@0.474900:0.271622:0.498506:0.271622:0.498506:0.251957:0.474900:0.251957:0.000000:0.000000:0.000000
⋅:@0.483833:0.272380:0.489573:0.272380:0.489573:0.252974:0.483833:0.252974:0.000000
−:@0.510861:0.272380:0.523468:0.272380:0.523468:0.252974:0.510861:0.252974:0.000000
):@0.534536:0.271622:0.541632:0.271622:0.541632:0.251957:0.534536:0.251957:0.000000
Norma y distancia:@0.108231:0.106238:0.254236:0.106238:0.254236:0.088555:0.108231:0.088555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.108231:0.123408:0.190607:0.123408:0.190607:0.106463:0.108231:0.106463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean u y v     ,  u = (u1, u2, u3 ) y  v = (v1, v2, v3,), :@0.190301:0.122946:0.551706:0.122946:0.551706:0.106448:0.190301:0.106448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.263355:0.122729:0.279403:0.122729:0.279403:0.108082:0.263355:0.108082:0.000000
R:@0.286858:0.121977:0.300768:0.121977:0.300768:0.108530:0.286858:0.108530:0.000000
3:@0.300564:0.116594:0.305517:0.116594:0.305517:0.106976:0.300564:0.106976:0.000000
la dis-:@0.551384:0.123408:0.595771:0.123408:0.595771:0.106463:0.551384:0.106463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tancia entre los puntos  u y v:@0.108245:0.140759:0.319822:0.140759:0.319822:0.123813:0.108245:0.123813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, se escribe como d(u, v) y se define por : :@0.319629:0.140297:0.599954:0.140297:0.599954:0.123799:0.319629:0.123799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d u v:@0.160678:0.173525:0.195230:0.173525:0.195230:0.157772:0.160678:0.157772:0.000000:0.000000:0.000000:0.000000:0.000000
( , ):@0.169837:0.173414:0.201071:0.173414:0.201071:0.157634:0.169837:0.157634:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.203707:0.174023:0.213823:0.174023:0.213823:0.158450:0.203707:0.158450:0.000000
(:@0.228787:0.173414:0.234481:0.173414:0.234481:0.157634:0.228787:0.157634:0.000000
u v:@0.233707:0.173525:0.268056:0.173525:0.268056:0.157772:0.233707:0.157772:0.000000:0.000000:0.000000
1:@0.241823:0.175546:0.246533:0.175546:0.246533:0.166401:0.241823:0.166401:0.000000
−:@0.249204:0.174023:0.259321:0.174023:0.259321:0.158450:0.249204:0.158450:0.000000
1:@0.267947:0.175546:0.272657:0.175546:0.272657:0.166401:0.267947:0.166401:0.000000
):@0.273025:0.173414:0.278719:0.173414:0.278719:0.157634:0.273025:0.157634:0.000000
2:@0.279046:0.165723:0.283755:0.165723:0.283755:0.156578:0.279046:0.156578:0.000000
+:@0.287159:0.174023:0.297275:0.174023:0.297275:0.158450:0.287159:0.158450:0.000000
(:@0.298989:0.173414:0.304683:0.173414:0.304683:0.157634:0.298989:0.157634:0.000000
u:@0.303909:0.173525:0.312718:0.173525:0.312718:0.157772:0.303909:0.157772:0.000000
2:@0.312497:0.175546:0.317206:0.175546:0.317206:0.166401:0.312497:0.166401:0.000000
−:@0.321030:0.174023:0.331147:0.174023:0.331147:0.158450:0.321030:0.158450:0.000000
v:@0.332437:0.173525:0.339882:0.173525:0.339882:0.157772:0.332437:0.157772:0.000000
2:@0.340244:0.175546:0.344953:0.175546:0.344953:0.166401:0.340244:0.166401:0.000000
):@0.346474:0.173414:0.352168:0.173414:0.352168:0.157634:0.346474:0.157634:0.000000
2:@0.352493:0.165723:0.357203:0.165723:0.357203:0.156578:0.352493:0.156578:0.000000
+:@0.360608:0.174023:0.370725:0.174023:0.370725:0.158450:0.360608:0.158450:0.000000
(:@0.372438:0.173414:0.378133:0.173414:0.378133:0.157634:0.372438:0.157634:0.000000
u:@0.377359:0.173525:0.386167:0.173525:0.386167:0.157772:0.377359:0.157772:0.000000
3:@0.385946:0.175546:0.390656:0.175546:0.390656:0.166401:0.385946:0.166401:0.000000
−:@0.394218:0.174023:0.404335:0.174023:0.404335:0.158450:0.394218:0.158450:0.000000
v:@0.405625:0.173525:0.413070:0.173525:0.413070:0.157772:0.405625:0.157772:0.000000
3:@0.413430:0.175546:0.418140:0.175546:0.418140:0.166401:0.413430:0.166401:0.000000
):@0.419399:0.173414:0.425093:0.173414:0.425093:0.157634:0.419399:0.157634:0.000000
2:@0.425420:0.165723:0.430129:0.165723:0.430129:0.156578:0.425420:0.156578:0.000000
=:@0.436151:0.174023:0.446268:0.174023:0.446268:0.158450:0.436151:0.158450:0.000000
(:@0.461231:0.173414:0.466925:0.173414:0.466925:0.157634:0.461231:0.157634:0.000000
u v u v:@0.466151:0.173525:0.543547:0.173525:0.543547:0.157772:0.466151:0.157772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
− ⋅ −:@0.476839:0.174023:0.534813:0.174023:0.534813:0.158450:0.476839:0.158450:0.000000:0.000000:0.000000:0.000000:0.000000
) (:@0.495838:0.173414:0.514782:0.173414:0.514782:0.157634:0.495838:0.157634:0.000000:0.000000:0.000000
):@0.543695:0.173414:0.549389:0.173414:0.549389:0.157634:0.543695:0.157634:0.000000
Competencia :@0.684408:0.104916:0.782031:0.104916:0.782031:0.089444:0.684408:0.089444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684408:0.117484:0.768471:0.117484:0.768471:0.102012:0.684408:0.102012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema:@0.684646:0.142381:0.745559:0.142381:0.745559:0.126909:0.684646:0.126909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  :@0.745525:0.141959:0.789870:0.141959:0.789870:0.126896:0.745525:0.126896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a, b :@0.638103:0.157801:0.664259:0.157801:0.664259:0.142738:0.638103:0.142738:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.664228:0.157452:0.678183:0.157452:0.678183:0.144715:0.664228:0.144715:0.000000
 :@0.678183:0.157603:0.682581:0.157603:0.682581:0.144229:0.678183:0.144229:0.000000
R:@0.682581:0.156798:0.694676:0.156798:0.694676:0.145105:0.682581:0.145105:0.000000
,  ,   ,:@0.694676:0.157801:0.729661:0.157801:0.729661:0.142738:0.694676:0.142738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.700903:0.157906:0.726564:0.157906:0.726564:0.142870:0.700903:0.142870:0.000000:0.000000:0.000000
 :@0.703594:0.158249:0.727145:0.158249:0.727145:0.143807:0.703594:0.143807:0.000000:0.000000:0.000000
:@0.729625:0.157452:0.743579:0.157452:0.743579:0.144715:0.729625:0.144715:0.000000
 :@0.743579:0.157603:0.747977:0.157603:0.747977:0.144229:0.743579:0.144229:0.000000
R:@0.747977:0.156798:0.760072:0.156798:0.760072:0.145105:0.747977:0.145105:0.000000
3:@0.760072:0.152000:0.764595:0.152000:0.764595:0.143218:0.760072:0.143218:0.000000
. :@0.764574:0.157801:0.770871:0.157801:0.770871:0.142738:0.764574:0.142738:0.000000:0.000000
Se verifican las propiedades :@0.638101:0.180772:0.819226:0.180772:0.819226:0.165708:0.638101:0.165708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguientes::@0.638101:0.196614:0.703816:0.196614:0.703816:0.181550:0.638101:0.181550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i.:@0.638101:0.219782:0.645014:0.219782:0.645014:0.204521:0.638101:0.204521:0.000000:0.000000
   (–a)   = –a  ;  :@0.644979:0.219584:0.752476:0.219582:0.752476:0.204519:0.644979:0.204521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.689311:0.219687:0.696417:0.219687:0.696417:0.204651:0.689311:0.204651:0.000000
:@0.691140:0.220031:0.696997:0.220031:0.696997:0.205589:0.691140:0.205589:0.000000
v:@0.734780:0.219687:0.741886:0.219687:0.741886:0.204651:0.734780:0.204651:0.000000
:@0.736609:0.220031:0.742467:0.220031:0.742467:0.205589:0.736609:0.205589:0.000000
ii.:@0.638106:0.235622:0.648871:0.235622:0.648871:0.220361:0.638106:0.220361:0.000000:0.000000:0.000000
   a(–  ) = –a  ;  :@0.648835:0.235424:0.754498:0.235424:0.754498:0.220361:0.648835:0.220361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.685935:0.235529:0.693041:0.235529:0.693041:0.220493:0.685935:0.220493:0.000000
:@0.687764:0.235873:0.693622:0.235873:0.693622:0.221431:0.687764:0.221431:0.000000
v:@0.736804:0.235529:0.743910:0.235529:0.743910:0.220493:0.736804:0.220493:0.000000
:@0.738633:0.235873:0.744490:0.235873:0.744490:0.221431:0.738633:0.221431:0.000000
iii.:@0.638105:0.251464:0.652722:0.251464:0.652722:0.236203:0.638105:0.236203:0.000000:0.000000:0.000000:0.000000
  (–a)(–  ) = a  ; :@0.652687:0.251266:0.761692:0.251266:0.761692:0.236203:0.652687:0.236203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.706391:0.251371:0.713497:0.251371:0.713497:0.236335:0.706391:0.236335:0.000000
:@0.708221:0.251715:0.714078:0.251715:0.714078:0.237273:0.708221:0.237273:0.000000
v:@0.747708:0.251371:0.754814:0.251371:0.754814:0.236335:0.747708:0.236335:0.000000
:@0.749537:0.251715:0.755394:0.251715:0.755394:0.237273:0.749537:0.237273:0.000000
iv.:@0.638105:0.267306:0.651913:0.267306:0.651913:0.252045:0.638105:0.252045:0.000000:0.000000:0.000000
  (a – b)   = a   – b  ;  :@0.651878:0.267108:0.797486:0.267108:0.797486:0.252045:0.651878:0.252045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.706743:0.267213:0.713849:0.267213:0.713849:0.252177:0.706743:0.252177:0.000000
:@0.708572:0.267557:0.714430:0.267557:0.714430:0.253115:0.708572:0.253115:0.000000
v:@0.742660:0.267213:0.749766:0.267213:0.749766:0.252177:0.742660:0.252177:0.000000
:@0.744490:0.267557:0.750347:0.267557:0.750347:0.253115:0.744490:0.253115:0.000000
v:@0.779792:0.267213:0.786898:0.267213:0.786898:0.252177:0.779792:0.252177:0.000000
:@0.781621:0.267557:0.787479:0.267557:0.787479:0.253115:0.781621:0.253115:0.000000
v.:@0.638103:0.283148:0.648129:0.283148:0.648129:0.267887:0.638103:0.267887:0.000000:0.000000
   a(  –   ) = a  – a  .:@0.648094:0.282950:0.785473:0.282950:0.785473:0.267887:0.648094:0.267887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.671862:0.283055:0.680270:0.283055:0.680270:0.268019:0.671862:0.268019:0.000000
:@0.674554:0.283399:0.680411:0.283399:0.680411:0.268957:0.674554:0.268957:0.000000
v:@0.701237:0.283055:0.708343:0.283055:0.708343:0.268019:0.701237:0.268019:0.000000
:@0.703066:0.283399:0.708923:0.283399:0.708923:0.268957:0.703066:0.268957:0.000000
u:@0.738773:0.283055:0.747181:0.283055:0.747181:0.268019:0.738773:0.268019:0.000000
:@0.741464:0.283399:0.747322:0.283399:0.747322:0.268957:0.741464:0.268957:0.000000
v:@0.775272:0.283055:0.782378:0.283055:0.782378:0.268019:0.775272:0.268019:0.000000
:@0.777101:0.283399:0.782959:0.283399:0.782959:0.268957:0.777101:0.268957:0.000000
Nota:@0.638104:0.306119:0.672193:0.306119:0.672193:0.290858:0.638104:0.290858:0.000000:0.000000:0.000000:0.000000
. Sean :@0.672158:0.305921:0.712650:0.305921:0.712650:0.290858:0.672158:0.290858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.674638:0.306343:0.678315:0.306343:0.678315:0.290871:0.674638:0.290871:0.000000
a:@0.712615:0.306026:0.720812:0.306026:0.720812:0.290990:0.712615:0.290990:0.000000
   :@0.720777:0.305723:0.743529:0.305722:0.743529:0.292348:0.720777:0.292350:0.000000:0.000000:0.000000
:@0.725177:0.305571:0.739132:0.305571:0.739132:0.292834:0.725177:0.292834:0.000000
R:@0.743529:0.304917:0.755624:0.304917:0.755624:0.293224:0.743529:0.293224:0.000000
,     :@0.755624:0.305920:0.781674:0.305920:0.781674:0.290856:0.755624:0.290856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.769345:0.306025:0.777752:0.306025:0.777752:0.290989:0.769345:0.290989:0.000000
:@0.772036:0.306368:0.777893:0.306368:0.777893:0.291926:0.772036:0.291926:0.000000
:@0.781674:0.305571:0.795629:0.305571:0.795629:0.292834:0.781674:0.292834:0.000000
 :@0.795629:0.305722:0.800027:0.305722:0.800027:0.292348:0.795629:0.292348:0.000000
R:@0.800027:0.304917:0.812122:0.304917:0.812122:0.293224:0.800027:0.293224:0.000000
3:@0.812120:0.300120:0.816642:0.300120:0.816642:0.291339:0.812120:0.291339:0.000000
. :@0.816643:0.305920:0.822941:0.305920:0.822941:0.290856:0.816643:0.290856:0.000000:0.000000
Los resultados  i),  ii),  iii) del  :@0.638105:0.328890:0.824682:0.328890:0.824682:0.313827:0.638105:0.313827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
teorema se conocen como regla :@0.638105:0.344732:0.849392:0.344732:0.849392:0.329669:0.638105:0.329669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los signos que a continua-:@0.638105:0.360574:0.825224:0.360574:0.825224:0.345511:0.638105:0.345511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción repetimos: :@0.638105:0.376416:0.741603:0.376416:0.741603:0.361353:0.638105:0.361353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(– )  = – ,:@0.701316:0.399386:0.783052:0.399386:0.783052:0.384323:0.701316:0.384323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a v:@0.716338:0.399492:0.737075:0.399492:0.737075:0.384455:0.716338:0.384455:0.000000:0.000000:0.000000
:@0.731798:0.399835:0.737656:0.399835:0.737656:0.385393:0.731798:0.385393:0.000000
av:@0.764673:0.399492:0.779958:0.399492:0.779958:0.384455:0.764673:0.384455:0.000000:0.000000
:@0.774681:0.399835:0.780538:0.399835:0.780538:0.385393:0.774681:0.385393:0.000000
a v:@0.701316:0.415334:0.731640:0.415334:0.731640:0.400297:0.701316:0.400297:0.000000:0.000000:0.000000
(– ) = – ,:@0.709513:0.415228:0.783052:0.415228:0.783052:0.400165:0.709513:0.400165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.726363:0.415677:0.732221:0.415677:0.732221:0.401235:0.726363:0.401235:0.000000
av:@0.764673:0.415334:0.779958:0.415334:0.779958:0.400297:0.764673:0.400297:0.000000:0.000000
:@0.774681:0.415677:0.780538:0.415677:0.780538:0.401235:0.774681:0.401235:0.000000
(– )(– ) =  .:@0.696321:0.431070:0.788046:0.431070:0.788046:0.416007:0.696321:0.416007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.710463:0.431176:0.718659:0.431176:0.718659:0.416139:0.710463:0.416139:0.000000
v:@0.739115:0.431176:0.746221:0.431176:0.746221:0.416139:0.739115:0.416139:0.000000
:@0.740945:0.431519:0.746802:0.431519:0.746802:0.417077:0.740945:0.417077:0.000000
av:@0.769668:0.431176:0.784953:0.431176:0.784953:0.416139:0.769668:0.416139:0.000000:0.000000
:@0.779676:0.431519:0.785533:0.431519:0.785533:0.417077:0.779676:0.417077:0.000000
Competencia digital:@0.684804:0.700178:0.827156:0.700178:0.827156:0.684705:0.684804:0.684705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para representar gráfica-:@0.685042:0.728805:0.841522:0.728805:0.841522:0.713742:0.685042:0.713742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mente puntos y vectores en el :@0.638498:0.744647:0.837985:0.744647:0.837985:0.729584:0.638498:0.729584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
espacio, :@0.638498:0.760489:0.693203:0.760489:0.693203:0.745426:0.638498:0.745426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
utiliza:@0.693203:0.760912:0.736877:0.760912:0.736877:0.745439:0.693203:0.745439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el :@0.736877:0.760489:0.755118:0.760489:0.755118:0.745426:0.736877:0.745426:0.000000:0.000000:0.000000:0.000000
software:@0.755118:0.760595:0.809083:0.760595:0.809083:0.745558:0.755118:0.745558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 libre, :@0.809086:0.760489:0.847274:0.760489:0.847274:0.745426:0.809086:0.745426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
GeoGebra, tal como se indica al :@0.638498:0.776331:0.849593:0.776331:0.849593:0.761268:0.638498:0.761268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
final de esta unidad.:@0.638498:0.792173:0.768153:0.792173:0.768153:0.777110:0.638498:0.777110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@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