212:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
M.5.2.18. Realizar las operaciones de adición entre elementos de :@0.143847:0.936137:0.426835:0.936137:0.426835:0.926095:0.143847:0.926095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.427550:0.935547:0.436017:0.935547:0.436017:0.927362:0.427550:0.927362:0.000000
3:@0.436010:0.932270:0.439025:0.932270:0.439025:0.926416:0.436010:0.926416:0.000000
 y de producto por un número escalar de manera geométrica y analítica, aplicando propiedades de los :@0.439026:0.936137:0.895014:0.936137:0.895014:0.926095:0.439026:0.926095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números reales; y reconocer los vectores como elementos geométricos de  .:@0.143842:0.946698:0.478087:0.946698:0.478087:0.936656:0.143842:0.936656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.464925:0.946108:0.473392:0.946108:0.473392:0.937923:0.464925:0.937923:0.000000
3:@0.473397:0.942832:0.476412:0.942832:0.476412:0.936977:0.473397:0.936977:0.000000
M.5.2.19. Calcular el producto escalar entre dos vectores y la norma de un vector para determinar la distancia entre dos puntos A y B en R^3, como la norma del vector AB.:@0.143842:0.955499:0.882650:0.955499:0.882650:0.945457:0.143842:0.945457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Producto escalar  :@0.404235:0.128379:0.626673:0.128379:0.626673:0.083720:0.404235:0.083720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e interpretación geométrica:@0.404235:0.166098:0.753170:0.166098:0.753170:0.121439:0.404235:0.121439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En lo sucesivo, a los elementos de   los denominamos escalares.:@0.404236:0.199611:0.859458:0.199611:0.859458:0.183113:0.404236:0.183113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.645509:0.198524:0.658814:0.198524:0.658814:0.185662:0.645509:0.185662:0.000000
Producto de escalares por elementos de :@0.404236:0.235710:0.727181:0.235710:0.727181:0.218027:0.404236:0.218027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.727181:0.233980:0.740485:0.233980:0.740485:0.221118:0.727181:0.221118:0.000000
3:@0.740485:0.228714:0.745438:0.228714:0.745438:0.219096:0.740485:0.219096:0.000000
Definición :@0.404236:0.252880:0.491103:0.252880:0.491103:0.235934:0.404236:0.235934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean       y   = ( ,  ,  )    . Se define el producto de   :@0.484322:0.252418:0.895913:0.252418:0.895913:0.235920:0.484322:0.235920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.527746:0.252533:0.536723:0.252533:0.536723:0.236065:0.527746:0.236065:0.000000
:@0.540274:0.251899:0.554927:0.251899:0.554927:0.238526:0.540274:0.238526:0.000000
R:@0.558482:0.251331:0.571787:0.251331:0.571787:0.238469:0.558482:0.238469:0.000000
u:@0.586727:0.252533:0.595936:0.252533:0.595936:0.236065:0.586727:0.236065:0.000000
:@0.589665:0.252909:0.596080:0.252909:0.596080:0.237091:0.589665:0.237091:0.000000
x y z:@0.619950:0.252533:0.654396:0.252533:0.654396:0.236065:0.619950:0.236065:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.663887:0.251899:0.678539:0.251899:0.678539:0.238526:0.663887:0.238526:0.000000
R:@0.682093:0.251331:0.695398:0.251331:0.695398:0.238469:0.682093:0.238469:0.000000
3:@0.695398:0.246065:0.700351:0.246065:0.700351:0.236447:0.695398:0.236447:0.000000
a:@0.882794:0.252533:0.891771:0.252533:0.891771:0.236065:0.882794:0.236065:0.000000
por  , que se escribe   ∙  , como sigue:   ∙   =   ∙ ( ,  ,  ) = ( ,  ,  ).:@0.404245:0.269768:0.891078:0.269768:0.891078:0.253271:0.404245:0.253271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.433682:0.269884:0.442891:0.269884:0.442891:0.253415:0.433682:0.253415:0.000000
:@0.436629:0.270260:0.443045:0.270260:0.443045:0.254442:0.436629:0.254442:0.000000
a u:@0.553855:0.269884:0.583080:0.269884:0.583080:0.253415:0.553855:0.253415:0.000000:0.000000:0.000000
:@0.576823:0.270260:0.583238:0.270260:0.583238:0.254442:0.576823:0.254442:0.000000
a u a x y z:@0.678813:0.269884:0.788856:0.269884:0.788856:0.253415:0.678813:0.253415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.701777:0.270260:0.708193:0.270260:0.708193:0.254442:0.701777:0.254442:0.000000
ax ay az:@0.819854:0.269884:0.882370:0.269884:0.882370:0.253415:0.819854:0.253415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la definición se sigue que el producto de un número real por un :@0.404264:0.304470:0.895848:0.304470:0.895848:0.287972:0.404264:0.287972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector de   es otro elemento de  , cuyos componentes son los pro-:@0.404264:0.321821:0.891781:0.321821:0.891781:0.305323:0.404264:0.305323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.474298:0.320734:0.487603:0.320734:0.487603:0.307872:0.474298:0.307872:0.000000
3:@0.487566:0.315468:0.492519:0.315468:0.492519:0.305850:0.487566:0.305850:0.000000
R:@0.639168:0.320734:0.652473:0.320734:0.652473:0.307872:0.639168:0.307872:0.000000
3:@0.652436:0.315468:0.657390:0.315468:0.657390:0.305850:0.652436:0.305850:0.000000
ductos del número real por los respectivos componentes del vector.:@0.404240:0.339171:0.884074:0.339171:0.884074:0.322674:0.404240:0.322674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El producto de escalares (números reales) por vectores de   es una :@0.404240:0.373873:0.895906:0.373873:0.895906:0.357375:0.404240:0.357375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.822934:0.372786:0.836239:0.372786:0.836239:0.359924:0.822934:0.359924:0.000000
3:@0.836239:0.367520:0.841192:0.367520:0.841192:0.357902:0.836239:0.357902:0.000000
operación que notamos “∙” y es una función de   ×   en  , definida :@0.404237:0.391224:0.895908:0.391224:0.895908:0.374726:0.404237:0.374726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R R:@0.735151:0.390137:0.779632:0.390137:0.779632:0.377275:0.735151:0.377275:0.000000:0.000000:0.000000
3:@0.779632:0.384871:0.784585:0.384871:0.784585:0.375253:0.779632:0.375253:0.000000
R:@0.809200:0.390137:0.822505:0.390137:0.822505:0.377275:0.809200:0.377275:0.000000
3:@0.822505:0.384871:0.827458:0.384871:0.827458:0.375253:0.822505:0.375253:0.000000
como sigue: :@0.404240:0.408574:0.492918:0.408574:0.492918:0.392077:0.404240:0.392077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∙ :                                   :@0.569324:0.443276:0.723946:0.443276:0.723946:0.426778:0.569324:0.426778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,  :@0.723946:0.455219:0.725258:0.453674:0.725258:0.437176:0.723946:0.438721:0.000000:0.000000:0.000000
 :@0.404240:0.460627:0.408382:0.460627:0.408382:0.444129:0.404240:0.444129:0.000000
con   ∙   arriba definido. Además, se asume que:@0.404240:0.477977:0.741301:0.477977:0.741301:0.461480:0.404240:0.461480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a u:@0.435334:0.478093:0.464559:0.478093:0.464559:0.461624:0.435334:0.461624:0.000000:0.000000:0.000000
:@0.456371:0.478469:0.463865:0.478469:0.463865:0.462651:0.456371:0.462651:0.000000
a u u a:@0.404240:0.495444:0.480395:0.495444:0.480395:0.478975:0.404240:0.478975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ∙   =   ∙   = ( ,  ,  ), donde      ,   = ( ,  ,  )    .:@0.413217:0.495328:0.803006:0.495328:0.803006:0.478831:0.413217:0.478831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.425277:0.495820:0.432771:0.495820:0.432771:0.480002:0.425277:0.480002:0.000000
:@0.452884:0.495820:0.460378:0.495820:0.460378:0.480002:0.452884:0.480002:0.000000
ax ay az:@0.505440:0.495444:0.567956:0.495444:0.567956:0.478975:0.505440:0.478975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.631837:0.495444:0.640815:0.495444:0.640815:0.478975:0.631837:0.478975:0.000000
:@0.644950:0.494810:0.659602:0.494810:0.659602:0.481436:0.644950:0.481436:0.000000
R:@0.663743:0.494241:0.677047:0.494241:0.677047:0.481379:0.663743:0.481379:0.000000
u:@0.683944:0.495444:0.693153:0.495444:0.693153:0.478975:0.683944:0.478975:0.000000
:@0.684965:0.495820:0.692459:0.495820:0.692459:0.480002:0.684965:0.480002:0.000000
x y z:@0.717504:0.495444:0.753107:0.495444:0.753107:0.478975:0.717504:0.478975:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.763200:0.494810:0.777852:0.494810:0.777852:0.481436:0.763200:0.481436:0.000000
R:@0.781994:0.494241:0.795299:0.494241:0.795299:0.481379:0.781994:0.481379:0.000000
3:@0.795297:0.488975:0.800251:0.488975:0.800251:0.479357:0.795297:0.479357:0.000000
Ejercicios resueltos:@0.404235:0.530406:0.534890:0.530406:0.534890:0.513619:0.404235:0.513619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404235:0.554726:0.416506:0.554726:0.416506:0.538011:0.404235:0.538011:0.000000:0.000000
  Para   = –2  y   =  –      ,       , –5  , se tiene   = –2  –      ,       , –5 :@0.416506:0.554509:0.890644:0.554509:0.890644:0.538011:0.416506:0.538011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.462454:0.554624:0.471432:0.554624:0.471432:0.538156:0.462454:0.538156:0.000000
u:@0.529767:0.554624:0.538976:0.554624:0.538976:0.538156:0.529767:0.538156:0.000000
:@0.532714:0.555000:0.539130:0.555000:0.539130:0.539182:0.532714:0.539182:0.000000
au:@0.728949:0.554624:0.746981:0.554624:0.746981:0.538156:0.728949:0.538156:0.000000:0.000000
:@0.740721:0.555000:0.747137:0.555000:0.747137:0.539182:0.740721:0.539182:0.000000
 :@0.404235:0.593244:0.408377:0.593244:0.408377:0.576747:0.404235:0.576747:0.000000
=  (–2)  –        , (–2)         , –2(–5)  =        , –       , 10  . :@0.427969:0.593244:0.796552:0.593244:0.796552:0.576747:0.427969:0.576747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404235:0.610595:0.408377:0.610595:0.408377:0.594097:0.404235:0.594097:0.000000
2.:@0.404235:0.635291:0.416506:0.635291:0.416506:0.618576:0.404235:0.618576:0.000000:0.000000
  Sean    = (5, 2, –1),    =   –1,     , –      . Entonces, :@0.416506:0.635074:0.768654:0.635074:0.768654:0.618576:0.416506:0.618576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.465768:0.635190:0.477038:0.635190:0.477038:0.618721:0.465768:0.618721:0.000000
:@0.468369:0.633050:0.475863:0.633050:0.475863:0.617232:0.468369:0.617232:0.000000
B:@0.565754:0.635190:0.574944:0.635190:0.574944:0.618721:0.565754:0.618721:0.000000
:@0.567238:0.633050:0.574732:0.633050:0.574732:0.617232:0.567238:0.617232:0.000000
3   – 20   = 3(5, 2, –1) – 20  –1,     , –      :@0.427969:0.670238:0.714943:0.670238:0.714943:0.653741:0.427969:0.653741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.436465:0.670354:0.447735:0.670354:0.447735:0.653885:0.436465:0.653885:0.000000
:@0.439066:0.668214:0.446560:0.668214:0.446560:0.652396:0.439066:0.652396:0.000000
B:@0.484551:0.670354:0.493741:0.670354:0.493741:0.653885:0.484551:0.653885:0.000000
:@0.486035:0.668214:0.493529:0.668214:0.493529:0.652396:0.486035:0.652396:0.000000
 :@0.404235:0.698274:0.408377:0.698274:0.408377:0.681776:0.404235:0.681776:0.000000
 :@0.427979:0.698274:0.432121:0.698274:0.432121:0.681776:0.427979:0.681776:0.000000
= (15, 6, –3) – (–20, 8, –5) = (35, –2, 2).:@0.501389:0.698274:0.778019:0.698274:0.778019:0.681776:0.501389:0.681776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedades del producto de escalares por elementos de :@0.404236:0.752491:0.859818:0.752491:0.859818:0.734808:0.404236:0.734808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.859818:0.750997:0.874332:0.750997:0.874332:0.736966:0.859818:0.736966:0.000000
3:@0.874330:0.745661:0.880038:0.745661:0.880038:0.735352:0.874330:0.735352:0.000000
Teorema :@0.404236:0.787012:0.477964:0.787012:0.477964:0.770066:0.404236:0.770066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Para todo  ,       y para todo  ,      , se verifican las :@0.471183:0.786549:0.895901:0.786549:0.895901:0.770052:0.471183:0.770052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.554349:0.786665:0.580398:0.786665:0.580398:0.770196:0.554349:0.770196:0.000000:0.000000:0.000000
:@0.585420:0.786031:0.600073:0.786031:0.600073:0.772657:0.585420:0.772657:0.000000
R:@0.605106:0.785462:0.618411:0.785462:0.618411:0.772600:0.605106:0.772600:0.000000
u v:@0.712693:0.786665:0.737642:0.786665:0.737642:0.770196:0.712693:0.770196:0.000000:0.000000:0.000000
 :@0.715660:0.787041:0.738277:0.787041:0.738277:0.771223:0.715660:0.771223:0.000000:0.000000:0.000000
:@0.743311:0.786031:0.757964:0.786031:0.757964:0.772657:0.743311:0.772657:0.000000
R:@0.762995:0.785462:0.776300:0.785462:0.776300:0.772600:0.762995:0.772600:0.000000
3:@0.776300:0.780196:0.781253:0.780196:0.781253:0.770578:0.776300:0.770578:0.000000
siguientes propiedades::@0.404233:0.803900:0.569103:0.803900:0.569103:0.787402:0.404233:0.787402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i.:@0.404233:0.838818:0.411843:0.838818:0.411843:0.822104:0.404233:0.822104:0.000000:0.000000
 :@0.411843:0.838602:0.415985:0.838602:0.415985:0.822104:0.411843:0.822104:0.000000
a bu:@0.427968:0.838717:0.461316:0.838717:0.461316:0.822248:0.427968:0.822248:0.000000:0.000000:0.000000:0.000000
( ) = ( )  =  ( ).:@0.436945:0.838602:0.586020:0.838602:0.586020:0.822104:0.436945:0.822104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.453610:0.839093:0.461104:0.839093:0.461104:0.823275:0.453610:0.823275:0.000000
ab u b au:@0.492102:0.838717:0.577524:0.838717:0.577524:0.822248:0.492102:0.822248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.517686:0.839093:0.525180:0.839093:0.525180:0.823275:0.517686:0.823275:0.000000
:@0.569818:0.839093:0.577312:0.839093:0.577312:0.823275:0.569818:0.823275:0.000000
ii.:@0.404233:0.863297:0.416100:0.863297:0.416100:0.846583:0.404233:0.846583:0.000000:0.000000:0.000000
  (  +  )  =   +  .:@0.416100:0.863081:0.563171:0.863081:0.563171:0.846583:0.416100:0.846583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b u au bu:@0.433921:0.863196:0.560628:0.863196:0.560628:0.846727:0.433921:0.846727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.478712:0.863572:0.486206:0.863572:0.486206:0.847754:0.478712:0.847754:0.000000
:@0.515625:0.863572:0.523119:0.863572:0.523119:0.847754:0.515625:0.847754:0.000000
:@0.552922:0.863572:0.560416:0.863572:0.560416:0.847754:0.552922:0.847754:0.000000
iii.:@0.404233:0.887776:0.420358:0.887776:0.420358:0.871062:0.404233:0.871062:0.000000:0.000000:0.000000:0.000000
  (  +  ) =   +  .:@0.420358:0.887560:0.561726:0.887560:0.561726:0.871062:0.420358:0.871062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a u v:@0.427968:0.887675:0.478770:0.887675:0.478770:0.871206:0.427968:0.871206:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.444401:0.888051:0.451895:0.888051:0.451895:0.872233:0.444401:0.872233:0.000000
:@0.472027:0.888051:0.479521:0.888051:0.479521:0.872233:0.472027:0.872233:0.000000
au av:@0.504566:0.887675:0.558220:0.887675:0.558220:0.871206:0.504566:0.871206:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.514892:0.888051:0.522387:0.888051:0.522387:0.872233:0.514892:0.872233:0.000000
:@0.551477:0.888051:0.558971:0.888051:0.558971:0.872233:0.551477:0.872233:0.000000
iv.:@0.404233:0.912255:0.419433:0.912255:0.419433:0.895541:0.404233:0.895541:0.000000:0.000000:0.000000
  1 ∙   =  .:@0.419433:0.912039:0.486418:0.912039:0.486418:0.895541:0.419433:0.895541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.447503:0.912154:0.455286:0.912154:0.455286:0.895686:0.447503:0.895686:0.000000
:@0.448543:0.912530:0.456037:0.912530:0.456037:0.896712:0.448543:0.896712:0.000000
v:@0.475129:0.912154:0.482912:0.912154:0.482912:0.895686:0.475129:0.895686:0.000000
:@0.476169:0.912530:0.483663:0.912530:0.483663:0.896712:0.476169:0.896712:0.000000
R:@0.605315:0.435236:0.618620:0.435236:0.618620:0.422374:0.605315:0.422374:0.000000
 ×      ,:@0.618620:0.436323:0.701408:0.436323:0.701408:0.419825:0.618620:0.419825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.637711:0.435236:0.651016:0.435236:0.651016:0.422374:0.637711:0.422374:0.000000
3:@0.651016:0.429971:0.655969:0.429971:0.655969:0.420353:0.651016:0.420353:0.000000
→:@0.660111:0.444422:0.676256:0.444422:0.676256:0.424559:0.660111:0.424559:0.000000
R:@0.680394:0.435236:0.693699:0.435236:0.693699:0.422374:0.680394:0.422374:0.000000
3:@0.693699:0.429971:0.698652:0.429971:0.698652:0.420353:0.693699:0.420353:0.000000
( ,  )           ∙ :@0.605313:0.453674:0.711753:0.453674:0.711753:0.437176:0.605313:0.437176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a u:@0.611266:0.453789:0.636349:0.453789:0.636349:0.437321:0.611266:0.437321:0.000000:0.000000:0.000000
:@0.630088:0.454165:0.636503:0.454165:0.636503:0.438347:0.630088:0.438347:0.000000
→:@0.671450:0.461773:0.687595:0.461773:0.687595:0.441910:0.671450:0.441910:0.000000
a u:@0.691737:0.453789:0.720962:0.453789:0.720962:0.437321:0.691737:0.437321:0.000000:0.000000:0.000000
:@0.714701:0.454165:0.721116:0.454165:0.721116:0.438347:0.714701:0.438347:0.000000
2:@0.581783:0.547101:0.590279:0.547101:0.590279:0.530604:0.581783:0.530604:0.000000
15 19:@0.577448:0.563440:0.625077:0.563440:0.625077:0.546942:0.577448:0.546942:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.812966:0.547101:0.821462:0.547101:0.821462:0.530604:0.812966:0.530604:0.000000
15 19:@0.808632:0.563440:0.856241:0.563440:0.856241:0.546942:0.808632:0.546942:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.506397:0.585533:0.514893:0.585533:0.514893:0.569036:0.506397:0.569036:0.000000
15:@0.502063:0.601872:0.519247:0.601872:0.519247:0.585374:0.502063:0.585374:0.000000:0.000000
2:@0.631183:0.628182:0.639679:0.628182:0.639679:0.611684:0.631183:0.611684:0.000000
5:@0.631183:0.644521:0.639679:0.644521:0.639679:0.628023:0.631183:0.628023:0.000000
2:@0.656311:0.663001:0.664807:0.663001:0.664807:0.646503:0.656311:0.646503:0.000000
5:@0.656311:0.679339:0.664807:0.679339:0.664807:0.662842:0.656311:0.662842:0.000000
1:@0.669857:0.628182:0.678353:0.628182:0.678353:0.611684:0.669857:0.611684:0.000000
4:@0.669857:0.644521:0.678353:0.644521:0.678353:0.628023:0.669857:0.628023:0.000000
1:@0.693309:0.663001:0.701805:0.663001:0.701805:0.646503:0.693309:0.646503:0.000000
4:@0.693309:0.679339:0.701805:0.679339:0.701805:0.662842:0.693309:0.662842:0.000000
4:@0.612227:0.547101:0.620723:0.547101:0.620723:0.530604:0.612227:0.530604:0.000000
4:@0.843410:0.547101:0.851906:0.547101:0.851906:0.530604:0.843410:0.530604:0.000000
4:@0.582073:0.585533:0.590569:0.585533:0.590569:0.569036:0.582073:0.569036:0.000000
19:@0.577738:0.601872:0.594923:0.601872:0.594923:0.585374:0.577738:0.585374:0.000000:0.000000
4:@0.697410:0.585533:0.705906:0.585533:0.705906:0.569036:0.697410:0.569036:0.000000
15:@0.693075:0.601872:0.710260:0.601872:0.710260:0.585374:0.693075:0.585374:0.000000:0.000000
8:@0.739867:0.585533:0.748363:0.585533:0.748363:0.569036:0.739867:0.569036:0.000000
19:@0.735532:0.601872:0.752717:0.601872:0.752717:0.585374:0.735532:0.585374:0.000000:0.000000
Saberes previos:@0.199646:0.112146:0.307805:0.112146:0.307805:0.096673:0.199646:0.096673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Son los escalares ele-:@0.199884:0.140773:0.339211:0.140773:0.339211:0.125710:0.199884:0.125710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mentos de  ?:@0.153341:0.156615:0.243891:0.156615:0.243891:0.141552:0.153341:0.141552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.226590:0.155612:0.238686:0.155612:0.238686:0.143919:0.226590:0.143919:0.000000
Desequilibrio cognitivo:@0.199646:0.203768:0.363493:0.203768:0.363493:0.188295:0.199646:0.188295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Es el producto escalar :@0.199884:0.232395:0.350117:0.232395:0.350117:0.217332:0.199884:0.217332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por elementos de   una ope-:@0.153341:0.248237:0.350523:0.248237:0.350523:0.233174:0.153341:0.233174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.271460:0.247234:0.283555:0.247234:0.283555:0.235542:0.271460:0.235542:0.000000
3:@0.283555:0.242437:0.288078:0.242437:0.288078:0.233655:0.283555:0.233655:0.000000
ración de composición interna?:@0.153339:0.264079:0.357453:0.264079:0.357453:0.249016:0.153339:0.249016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.379343:0.297267:0.379343:0.297267:0.363871:0.199644:0.363871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.391911:0.283707:0.391911:0.283707:0.376439:0.199644:0.376439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Algunas propiedades del :@0.199880:0.416386:0.362919:0.416386:0.362919:0.401323:0.199880:0.401323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto “ ∙ ” de números reales :@0.153337:0.432228:0.363659:0.432228:0.363659:0.417165:0.153337:0.417165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son::@0.153337:0.448070:0.179212:0.448070:0.179212:0.433007:0.153337:0.433007:0.000000:0.000000:0.000000:0.000000
•:@0.153337:0.471688:0.160426:0.471688:0.160426:0.455991:0.153337:0.455991:0.000000
 :@0.160426:0.471041:0.164208:0.471041:0.164208:0.455978:0.160426:0.455978:0.000000
Conmutativa: :@0.169960:0.471147:0.260388:0.471147:0.260388:0.456110:0.169960:0.456110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para todo  :@0.260388:0.471041:0.332312:0.471041:0.332312:0.455978:0.260388:0.455978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.153337:0.486883:0.157119:0.486883:0.157119:0.471820:0.153337:0.471820:0.000000
x y:@0.169960:0.486989:0.190100:0.486989:0.190100:0.471952:0.169960:0.471952:0.000000:0.000000:0.000000
,   :@0.176785:0.486883:0.193882:0.486883:0.193882:0.471820:0.176785:0.471820:0.000000:0.000000:0.000000:0.000000
:@0.193886:0.486533:0.207841:0.486533:0.207841:0.473796:0.193886:0.473796:0.000000
 :@0.207841:0.486684:0.212239:0.486684:0.212239:0.473310:0.207841:0.473310:0.000000
R:@0.212239:0.485879:0.224334:0.485879:0.224334:0.474186:0.212239:0.474186:0.000000
,     ∙   =   ∙  .:@0.224332:0.486882:0.305985:0.486882:0.305985:0.471819:0.224332:0.471819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y y x:@0.238193:0.486987:0.303470:0.486987:0.303470:0.471951:0.238193:0.471951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153339:0.510499:0.160428:0.510499:0.160428:0.494803:0.153339:0.494803:0.000000
 :@0.160428:0.509853:0.164210:0.509853:0.164210:0.494789:0.160428:0.494789:0.000000
Asociativa: :@0.169961:0.509958:0.242151:0.509958:0.242151:0.494921:0.169961:0.494921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para todo:@0.242151:0.509853:0.306513:0.509853:0.306513:0.494789:0.242151:0.494789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.153339:0.525695:0.157121:0.525695:0.157121:0.510631:0.153339:0.510631:0.000000
x y z:@0.169961:0.525800:0.201588:0.525800:0.201588:0.510763:0.169961:0.510763:0.000000:0.000000:0.000000:0.000000:0.000000
,  ,   :@0.176786:0.525695:0.205370:0.525695:0.205370:0.510631:0.176786:0.510631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.204933:0.525346:0.218888:0.525346:0.218888:0.512609:0.204933:0.512609:0.000000
 :@0.218886:0.525496:0.223283:0.525496:0.223283:0.512123:0.218886:0.512123:0.000000
R:@0.222773:0.524692:0.234868:0.524692:0.234868:0.512999:0.222773:0.512999:0.000000
,    ∙ ( ∙  ) = (  ∙  ) ∙  .:@0.234868:0.525695:0.361498:0.525695:0.361498:0.510631:0.234868:0.510631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y  z:@0.244067:0.525800:0.287814:0.525800:0.287814:0.510763:0.244067:0.510763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y   z:@0.315237:0.525800:0.358983:0.525800:0.358983:0.510763:0.315237:0.510763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153338:0.549312:0.160427:0.549312:0.160427:0.533616:0.153338:0.533616:0.000000
 :@0.160427:0.548665:0.164209:0.548665:0.164209:0.533602:0.160427:0.533602:0.000000
Existencia de elemento :@0.169961:0.548771:0.316132:0.548771:0.316132:0.533734:0.169961:0.533734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
unidad: :@0.169961:0.564613:0.221394:0.564613:0.221394:0.549576:0.169961:0.549576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
existe 1 :@0.221394:0.564507:0.273021:0.564507:0.273021:0.549444:0.221394:0.549444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.273023:0.564157:0.286978:0.564157:0.286978:0.551421:0.273023:0.551421:0.000000
 :@0.286978:0.564308:0.291375:0.564308:0.291375:0.550935:0.286978:0.550935:0.000000
R:@0.291375:0.563503:0.303471:0.563503:0.303471:0.551811:0.291375:0.551811:0.000000
, tal que :@0.303471:0.564506:0.358422:0.564506:0.358422:0.549443:0.303471:0.549443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para todo   :@0.169962:0.580348:0.248711:0.580348:0.248711:0.565285:0.169962:0.565285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.238104:0.580454:0.244929:0.580454:0.244929:0.565417:0.238104:0.565417:0.000000
:@0.248714:0.579999:0.262668:0.579999:0.262668:0.567263:0.248714:0.567263:0.000000
 :@0.262668:0.580150:0.267066:0.580150:0.267066:0.566777:0.262668:0.566777:0.000000
R:@0.267066:0.579345:0.279161:0.579345:0.279161:0.567653:0.267066:0.567653:0.000000
, 1 ∙   =  .:@0.279159:0.580348:0.336890:0.580348:0.336890:0.565285:0.279159:0.565285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  x x:@0.293214:0.580454:0.334374:0.580454:0.334374:0.565417:0.293214:0.565417:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153338:0.603966:0.160427:0.603966:0.160427:0.588269:0.153338:0.588269:0.000000
 :@0.160427:0.603319:0.164209:0.603319:0.164209:0.588256:0.160427:0.588256:0.000000
Existencia de opuestos multi-:@0.169961:0.603425:0.351314:0.603425:0.351314:0.588388:0.169961:0.588388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
plicativos: :@0.169961:0.619267:0.235341:0.619267:0.235341:0.604230:0.169961:0.604230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para cada   :@0.235341:0.619161:0.312665:0.619161:0.312665:0.604098:0.235341:0.604098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.302058:0.619267:0.308883:0.619267:0.308883:0.604230:0.302058:0.604230:0.000000
:@0.312669:0.618811:0.326624:0.618811:0.326624:0.606074:0.312669:0.606074:0.000000
 :@0.326624:0.618962:0.331022:0.618962:0.331022:0.605588:0.326624:0.605588:0.000000
R:@0.331022:0.618157:0.343117:0.618157:0.343117:0.606464:0.331022:0.606464:0.000000
, :@0.343115:0.619160:0.349412:0.619160:0.349412:0.604097:0.343115:0.604097:0.000000:0.000000
x:@0.169959:0.635107:0.176784:0.635107:0.176784:0.620071:0.169959:0.620071:0.000000
 ≠ 0, existe:@0.176784:0.635002:0.244576:0.635002:0.244576:0.619939:0.176784:0.619939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.153336:0.662408:0.157118:0.662408:0.157118:0.647345:0.153336:0.647345:0.000000
x:@0.169959:0.662514:0.176784:0.662514:0.176784:0.647477:0.169959:0.647477:0.000000
–1:@0.176789:0.656614:0.186900:0.656614:0.186900:0.647832:0.176789:0.647832:0.000000:0.000000
 =   :@0.186901:0.662415:0.222370:0.662408:0.222370:0.647345:0.186901:0.647352:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.207576:0.655068:0.215334:0.655068:0.215334:0.640005:0.207576:0.640005:0.000000
x:@0.208051:0.671518:0.214876:0.671518:0.214876:0.656481:0.208051:0.656481:0.000000
:@0.222359:0.662066:0.236314:0.662066:0.236314:0.649329:0.222359:0.649329:0.000000
 :@0.236314:0.662217:0.240711:0.662217:0.240711:0.648843:0.236314:0.648843:0.000000
R:@0.240711:0.661412:0.252806:0.661412:0.252806:0.649719:0.240711:0.649719:0.000000
, tal que :@0.252806:0.662415:0.307757:0.662415:0.307757:0.647352:0.252806:0.647352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xx:@0.307757:0.662520:0.321407:0.662520:0.321407:0.647484:0.307757:0.647484:0.000000:0.000000
–1:@0.321406:0.656614:0.331517:0.656614:0.331517:0.647832:0.321406:0.647832:0.000000:0.000000
 = 1. :@0.331517:0.662415:0.363004:0.662415:0.363004:0.647352:0.331517:0.647352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  Al conjunto   provisto de :@0.153348:0.694099:0.344044:0.694099:0.344044:0.679036:0.153348:0.679036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.251476:0.693096:0.263571:0.693096:0.263571:0.681403:0.251476:0.681403:0.000000
la operación producto “ ∙ ”, y :@0.169957:0.709941:0.355775:0.709941:0.355775:0.694878:0.169957:0.694878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que verifica las propiedades :@0.169957:0.725783:0.353031:0.725783:0.353031:0.710720:0.169957:0.710720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i) a iv) precedentes, lo de-:@0.169957:0.741625:0.336813:0.741625:0.336813:0.726562:0.169957:0.726562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nominamos grupo conmu-:@0.169957:0.757467:0.347210:0.757467:0.347210:0.742404:0.169957:0.742404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tativo para el producto, y lo :@0.169957:0.773309:0.353279:0.773309:0.353279:0.758246:0.169957:0.758246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denotamos como (  – {0}, ∙). :@0.169957:0.789151:0.363955:0.789151:0.363955:0.774088:0.169957:0.774088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.295712:0.788148:0.307808:0.788148:0.307808:0.776455:0.295712:0.776455:0.000000
 :@0.153350:0.804993:0.157132:0.804993:0.157132:0.789930:0.153350:0.789930:0.000000
x y z:@0.169972:0.805098:0.202479:0.805098:0.202479:0.790062:0.169972:0.790062:0.000000:0.000000:0.000000:0.000000:0.000000
,  ,   :@0.176797:0.804993:0.206261:0.804993:0.206261:0.789930:0.176797:0.789930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.206251:0.804644:0.220206:0.804644:0.220206:0.791907:0.206251:0.791907:0.000000
 :@0.220206:0.804795:0.224604:0.804795:0.224604:0.791421:0.220206:0.791421:0.000000
R:@0.224604:0.803990:0.236699:0.803990:0.236699:0.792297:0.224604:0.792297:0.000000
.:@0.236699:0.804993:0.239214:0.804993:0.239214:0.789930:0.236699:0.789930:0.000000
•:@0.153340:0.828610:0.160428:0.828610:0.160428:0.812914:0.153340:0.812914:0.000000
  La adición y el producto de :@0.160428:0.827964:0.351241:0.827964:0.351241:0.812900:0.160428:0.812900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números reales están ligados :@0.169962:0.843805:0.358717:0.843805:0.358717:0.828742:0.169962:0.828742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por la propiedad distributiva: :@0.169962:0.859647:0.361567:0.859647:0.361567:0.844584:0.169962:0.844584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para todo  ,  ,   :@0.169962:0.875489:0.274393:0.875489:0.274393:0.860426:0.169962:0.860426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.238104:0.875595:0.270611:0.875595:0.270611:0.860558:0.238104:0.860558:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.274393:0.875139:0.288348:0.875139:0.288348:0.862403:0.274393:0.862403:0.000000
 :@0.288348:0.875290:0.292746:0.875290:0.292746:0.861917:0.288348:0.861917:0.000000
R:@0.292746:0.874486:0.304841:0.874486:0.304841:0.862793:0.292746:0.862793:0.000000
, :@0.304841:0.875488:0.311138:0.875488:0.311138:0.860425:0.304841:0.860425:0.000000:0.000000
 :@0.153338:0.898459:0.157120:0.898459:0.157120:0.883396:0.153338:0.883396:0.000000
x y z:@0.209433:0.898565:0.252212:0.898565:0.252212:0.883528:0.209433:0.883528:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) =      .:@0.216258:0.898459:0.322009:0.898459:0.322009:0.883396:0.216258:0.883396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xy + xz:@0.275079:0.898565:0.319493:0.898565:0.319493:0.883528:0.275079:0.883528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000