81:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
Producto escalar o producto punto de dos vectores:@0.108233:0.106238:0.519108:0.106238:0.519108:0.088555:0.108233:0.088555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108233:0.130536:0.188317:0.130536:0.188317:0.113590:0.108233:0.113590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,     de  . Se define el producto escalar de   con  , que :@0.108233:0.154552:0.599905:0.154553:0.599905:0.138055:0.108233:0.138055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.149223:0.154669:0.177699:0.154669:0.177699:0.138200:0.149223:0.138200:0.000000:0.000000:0.000000
:@0.185784:0.154336:0.201832:0.154336:0.201832:0.139689:0.185784:0.139689:0.000000
V:@0.230056:0.154669:0.240806:0.154669:0.240806:0.138200:0.230056:0.138200:0.000000
2 :@0.240818:0.157224:0.247545:0.157224:0.247545:0.148442:0.240818:0.148442:0.000000:0.000000
u:@0.495483:0.154669:0.504692:0.154669:0.504692:0.138200:0.495483:0.138200:0.000000
v:@0.548148:0.154669:0.555931:0.154669:0.555931:0.138200:0.548148:0.138200:0.000000
se denota :@0.108236:0.172526:0.181722:0.172526:0.181722:0.156028:0.108236:0.156028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.197880:0.173169:0.202696:0.173169:0.202696:0.156888:0.197880:0.156888:0.000000
uv:@0.186048:0.172648:0.211574:0.172648:0.211574:0.156179:0.186048:0.156179:0.000000:0.000000
 como :@0.216464:0.172532:0.266099:0.172532:0.266099:0.156035:0.216464:0.156035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos:@0.374243:0.172532:0.397284:0.172532:0.397284:0.156035:0.374243:0.156035:0.000000:0.000000:0.000000
θ:@0.403130:0.173169:0.413167:0.173169:0.417939:0.156888:0.407902:0.156888:0.000000
():@0.398901:0.176202:0.423117:0.176202:0.423117:0.154711:0.398901:0.154711:0.000000:0.000000
⋅=:@0.279644:0.173169:0.309177:0.173169:0.309177:0.156888:0.279644:0.156888:0.000000:0.000000
uv:@0.267815:0.172648:0.293765:0.172648:0.293765:0.156179:0.267815:0.156179:0.000000:0.000000
u:@0.319754:0.172648:0.328963:0.172648:0.328963:0.156179:0.319754:0.156179:0.000000
v:@0.355202:0.172648:0.362985:0.172648:0.362985:0.156179:0.355202:0.156179:0.000000
, donde :@0.426483:0.172532:0.483979:0.172532:0.483979:0.156035:0.426483:0.156035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,:@0.525013:0.172532:0.537670:0.172532:0.537670:0.156035:0.525013:0.156035:0.000000:0.000000
θ:@0.483643:0.173169:0.493681:0.173169:0.498453:0.156888:0.488416:0.156888:0.000000
π:@0.537875:0.173169:0.548452:0.173169:0.553224:0.156888:0.542647:0.156888:0.000000
[:@0.517893:0.175958:0.524308:0.175958:0.524308:0.154793:0.517893:0.154793:0.000000
]:@0.552647:0.175958:0.559063:0.175958:0.559063:0.154793:0.552647:0.154793:0.000000
∈:@0.500197:0.173169:0.513933:0.173169:0.513933:0.156888:0.500197:0.156888:0.000000
 es el :@0.562289:0.172532:0.599914:0.172532:0.599914:0.156035:0.562289:0.156035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ángulo que forman los vectores   con  .:@0.108246:0.189883:0.399233:0.189883:0.399233:0.173386:0.108246:0.173386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.338150:0.189999:0.347358:0.189999:0.347358:0.173530:0.338150:0.173530:0.000000
v:@0.386944:0.189999:0.394728:0.189999:0.394728:0.173530:0.386944:0.173530:0.000000
Para el caso particular :@0.108231:0.213943:0.266917:0.213943:0.266917:0.197445:0.108231:0.197445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.282520:0.214577:0.293097:0.214577:0.293097:0.198296:0.282520:0.198296:0.000000
uv:@0.269073:0.214056:0.304232:0.214056:0.304232:0.197587:0.269073:0.197587:0.000000:0.000000
, se obtiene :@0.306015:0.213940:0.390358:0.213940:0.390358:0.197443:0.306015:0.197443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.417265:0.214577:0.427841:0.214577:0.427841:0.198296:0.417265:0.198296:0.000000
⋅:@0.455795:0.214577:0.460611:0.214577:0.460611:0.198296:0.455795:0.198296:0.000000
u:@0.398153:0.214056:0.407362:0.214056:0.407362:0.197587:0.398153:0.197587:0.000000
u u:@0.443966:0.214056:0.470658:0.214056:0.470658:0.197587:0.443966:0.197587:0.000000:0.000000:0.000000
.:@0.473162:0.213940:0.475917:0.213940:0.475917:0.197443:0.473162:0.197443:0.000000
El espacio vectorial   provisto del producto escalar se llama espacio :@0.108220:0.234848:0.599854:0.234856:0.599854:0.218358:0.108220:0.218350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.248014:0.234964:0.258764:0.234964:0.258764:0.218495:0.248014:0.218495:0.000000
2:@0.258794:0.237527:0.263316:0.237527:0.263316:0.228745:0.258794:0.228745:0.000000
euclídeo  .:@0.108230:0.252206:0.193137:0.252206:0.193137:0.235709:0.108230:0.235709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.172901:0.252322:0.183651:0.252322:0.183651:0.235853:0.172901:0.235853:0.000000
2 :@0.183656:0.254878:0.190383:0.254878:0.190383:0.246096:0.183656:0.246096:0.000000:0.000000
Ejercicio resuelto:@0.108235:0.277061:0.226213:0.277061:0.226213:0.260275:0.108235:0.260275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dados los vectores  ,:@0.108235:0.294658:0.263254:0.294664:0.263254:0.278167:0.108235:0.278160:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.301385:0.296883:0.306302:0.296883:0.306302:0.287334:0.301385:0.287334:0.000000
∈:@0.279397:0.295300:0.293133:0.295300:0.293133:0.279020:0.279397:0.279020:0.000000
uv V:@0.249247:0.294780:0.303036:0.294780:0.303036:0.278311:0.249247:0.278311:0.000000:0.000000:0.000000:0.000000
, donde :@0.310761:0.294664:0.369096:0.294664:0.369096:0.278167:0.310761:0.278167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.401628:0.295300:0.352367:0.295300:0.352367:0.279020:0.401628:0.279020:0.000000
=:@0.461466:0.295300:0.412204:0.295300:0.412204:0.279020:0.461466:0.279020:0.000000
u:@0.379897:0.294780:0.389105:0.294780:0.389105:0.278311:0.379897:0.278311:0.000000
v:@0.440158:0.294780:0.447942:0.294780:0.447942:0.278311:0.440158:0.278311:0.000000
2,:@0.415710:0.294664:0.428367:0.294664:0.428367:0.278167:0.415710:0.278167:0.000000:0.000000
1,  es un vector :@0.474758:0.294664:0.599921:0.294664:0.599921:0.278167:0.474758:0.278167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.494780:0.294780:0.502563:0.294780:0.502563:0.278311:0.494780:0.278311:0.000000
horizontal y  forma un ángulo de 120° respecto de la horizontal y en :@0.108233:0.312015:0.599879:0.312015:0.599879:0.295517:0.108233:0.295517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.198177:0.312131:0.207385:0.312131:0.207385:0.295662:0.198177:0.295662:0.000000
el sentido antihorario (ver figura 2.23.), calcula la norma y determina el :@0.108231:0.329366:0.599902:0.329366:0.599902:0.312868:0.108231:0.312868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ángulo que forma el vector resultante respecto de la horizontal y en el :@0.108231:0.346716:0.599912:0.346716:0.599912:0.330219:0.108231:0.330219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sentido antihorario para :@0.108231:0.364067:0.279268:0.364067:0.279268:0.347570:0.108231:0.347570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.312632:0.364067:0.321128:0.364067:0.321128:0.347570:0.312632:0.347570:0.000000
2 .:@0.346501:0.364067:0.368807:0.364067:0.368807:0.347570:0.346501:0.347570:0.000000:0.000000:0.000000
α:@0.279587:0.364703:0.291744:0.364703:0.296516:0.348423:0.284360:0.348423:0.000000
=:@0.298550:0.364703:0.309127:0.364703:0.309127:0.348423:0.298550:0.348423:0.000000
−:@0.333209:0.364703:0.343785:0.364703:0.343785:0.348423:0.333209:0.348423:0.000000
u:@0.320532:0.364183:0.329741:0.364183:0.329741:0.347714:0.320532:0.347714:0.000000
v:@0.356192:0.364183:0.363975:0.364183:0.363975:0.347714:0.356192:0.347714:0.000000
=:@0.134199:0.391276:0.144776:0.391276:0.144776:0.374996:0.134199:0.374996:0.000000
+:@0.177450:0.391276:0.188026:0.391276:0.188026:0.374996:0.177450:0.374996:0.000000
=:@0.243934:0.391276:0.254511:0.391276:0.254511:0.374996:0.243934:0.374996:0.000000
a:@0.116880:0.390756:0.125857:0.390756:0.125857:0.374287:0.116880:0.374287:0.000000
5:@0.160130:0.390640:0.168626:0.390640:0.168626:0.374143:0.160130:0.374143:0.000000
(33):@0.189972:0.390640:0.232259:0.390640:0.232259:0.374143:0.189972:0.374143:0.000000:0.000000:0.000000:0.000000
2 13.:@0.257246:0.390640:0.299985:0.390640:0.299985:0.374143:0.257246:0.374143:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.168803:0.382605:0.173721:0.382605:0.173721:0.373056:0.168803:0.373056:0.000000
2:@0.232563:0.382605:0.237480:0.382605:0.237480:0.373056:0.232563:0.373056:0.000000
Se tiene :@0.108238:0.422248:0.168423:0.422248:0.168423:0.405750:0.108238:0.405750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.204801:0.423065:0.166726:0.423065:0.166726:0.406077:0.204801:0.406077:0.000000
=:@0.253912:0.423065:0.215837:0.423065:0.215837:0.406077:0.253912:0.406077:0.000000
=:@0.323952:0.423065:0.285616:0.423065:0.285616:0.406077:0.323952:0.406077:0.000000
=:@0.373325:0.423065:0.334988:0.423065:0.334988:0.406077:0.373325:0.406077:0.000000
3:@0.176898:0.422402:0.185763:0.422402:0.185763:0.405187:0.176898:0.405187:0.000000
3:@0.218732:0.422402:0.227597:0.422402:0.227597:0.405187:0.218732:0.405187:0.000000
6, 2:@0.268245:0.422402:0.304652:0.422402:0.304652:0.405187:0.268245:0.405187:0.000000:0.000000:0.000000:0.000000
2:@0.337882:0.422402:0.346747:0.422402:0.346747:0.405187:0.337882:0.405187:0.000000
2:@0.387234:0.422402:0.396100:0.422402:0.396100:0.405187:0.387234:0.405187:0.000000
u:@0.185160:0.422522:0.194769:0.422522:0.194769:0.405337:0.185160:0.405337:0.000000
u:@0.234271:0.422522:0.243881:0.422522:0.243881:0.405337:0.234271:0.405337:0.000000
v:@0.304739:0.422522:0.312860:0.422522:0.312860:0.405337:0.304739:0.405337:0.000000
v:@0.354111:0.422522:0.362233:0.422522:0.362233:0.405337:0.354111:0.405337:0.000000
.:@0.399599:0.422241:0.402354:0.422241:0.402354:0.405744:0.399599:0.405744:0.000000
Ángulo que forman los vectores :@0.108231:0.443149:0.340029:0.443149:0.340029:0.426651:0.108231:0.426651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.378821:0.443981:0.389858:0.443981:0.389858:0.426992:0.378821:0.426992:0.000000
3y 2:@0.342535:0.443317:0.400552:0.443317:0.400552:0.426102:0.342535:0.426102:0.000000:0.000000:0.000000:0.000000
u:@0.350814:0.443437:0.360424:0.443437:0.360424:0.426253:0.350814:0.426253:0.000000
v:@0.400649:0.443437:0.408771:0.443437:0.408771:0.426253:0.400649:0.426253:0.000000
: 120º.:@0.413740:0.443156:0.455468:0.443156:0.455468:0.426659:0.413740:0.426659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por la ley de los cosenos::@0.108231:0.464064:0.282195:0.464064:0.282195:0.447566:0.108231:0.447566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.143622:0.490171:0.154659:0.490171:0.154659:0.473183:0.143622:0.473183:0.000000
+ −:@0.197438:0.490171:0.227331:0.490171:0.227331:0.473183:0.197438:0.473183:0.000000:0.000000:0.000000
−:@0.261787:0.490171:0.272824:0.490171:0.272824:0.473183:0.261787:0.473183:0.000000
−:@0.323081:0.490171:0.334117:0.490171:0.334117:0.473183:0.323081:0.473183:0.000000
=:@0.136144:0.518536:0.147181:0.518536:0.147181:0.501547:0.136144:0.501547:0.000000
3:@0.163524:0.489508:0.172390:0.489508:0.172390:0.472293:0.163524:0.472293:0.000000
2:@0.227190:0.489508:0.236056:0.489508:0.236056:0.472293:0.227190:0.472293:0.000000
23:@0.274673:0.489508:0.299922:0.489508:0.299922:0.472293:0.274673:0.472293:0.000000:0.000000
2cos(120º):@0.333997:0.489508:0.430350:0.489508:0.430350:0.472293:0.333997:0.472293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
213.:@0.150076:0.517872:0.194302:0.517872:0.194302:0.500657:0.150076:0.500657:0.000000:0.000000:0.000000:0.000000
2:@0.133362:0.478651:0.138487:0.478651:0.138487:0.468698:0.133362:0.468698:0.000000
2:@0.188647:0.478651:0.193773:0.478651:0.193773:0.468698:0.188647:0.468698:0.000000
2:@0.252568:0.478651:0.257694:0.478651:0.257694:0.468698:0.252568:0.468698:0.000000
a:@0.117133:0.489628:0.126501:0.489628:0.126501:0.472443:0.117133:0.472443:0.000000
u:@0.171792:0.489628:0.181402:0.489628:0.181402:0.472443:0.171792:0.472443:0.000000
v:@0.236122:0.489628:0.244243:0.489628:0.244243:0.472443:0.236122:0.472443:0.000000
u:@0.299305:0.489628:0.308914:0.489628:0.308914:0.472443:0.299305:0.472443:0.000000
v:@0.342908:0.489628:0.351030:0.489628:0.351030:0.472443:0.342908:0.472443:0.000000
a:@0.117113:0.517993:0.126481:0.517993:0.126481:0.500808:0.117113:0.500808:0.000000
Por la ley de senos: :@0.108233:0.546763:0.245188:0.546763:0.245188:0.530265:0.108233:0.530265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.187015:0.581135:0.197963:0.581135:0.197963:0.564282:0.187015:0.564282:0.000000
α:@0.232821:0.592480:0.245405:0.592480:0.245405:0.575627:0.232821:0.575627:0.000000
α=:@0.140430:0.627592:0.173713:0.627592:0.173713:0.610739:0.140430:0.610739:0.000000:0.000000
=:@0.262635:0.627592:0.273583:0.627592:0.273583:0.610739:0.262635:0.610739:0.000000
α=:@0.110736:0.661193:0.138296:0.661193:0.138296:0.644340:0.110736:0.644340:0.000000:0.000000
sen:@0.113129:0.591941:0.136521:0.591941:0.136521:0.574894:0.113129:0.574894:0.000000:0.000000:0.000000
sen:@0.203945:0.591941:0.227357:0.591941:0.227357:0.574894:0.203945:0.574894:0.000000:0.000000:0.000000
sen:@0.111574:0.627053:0.134966:0.627053:0.134966:0.610006:0.111574:0.610006:0.000000:0.000000:0.000000
sen:@0.188729:0.617355:0.212122:0.617355:0.212122:0.600308:0.188729:0.600308:0.000000:0.000000:0.000000
213:@0.126809:0.570778:0.166036:0.570778:0.166036:0.553701:0.126809:0.553701:0.000000:0.000000:0.000000
(120º):@0.136262:0.591821:0.182049:0.591821:0.182049:0.574744:0.136262:0.574744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.222890:0.570778:0.231685:0.570778:0.231685:0.553701:0.222890:0.553701:0.000000
():@0.227098:0.591821:0.251746:0.591821:0.251746:0.574744:0.227098:0.574744:0.000000:0.000000
():@0.134707:0.626934:0.159355:0.626934:0.159355:0.609856:0.134707:0.609856:0.000000:0.000000
2:@0.178858:0.617235:0.187653:0.617235:0.187653:0.600158:0.178858:0.600158:0.000000
(120º):@0.211882:0.617235:0.257669:0.617235:0.257669:0.600158:0.211882:0.600158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
213:@0.197923:0.639416:0.237149:0.639416:0.237149:0.622339:0.197923:0.622339:0.000000:0.000000:0.000000
39:@0.292229:0.617235:0.309738:0.617235:0.309738:0.600158:0.292229:0.600158:0.000000:0.000000
26:@0.286266:0.638279:0.303775:0.638279:0.303775:0.621201:0.286266:0.621201:0.000000:0.000000
13,89788625.:@0.141068:0.660534:0.239602:0.660534:0.239602:0.643457:0.141068:0.643457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El ángulo del vector resultante es: Ω = 13,9° + 120° = 133,9°, medido :@0.108233:0.687834:0.600013:0.687834:0.600013:0.671336:0.108233:0.671336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en sentido antihorario.:@0.108233:0.705184:0.268632:0.705184:0.268632:0.688687:0.108233:0.688687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El producto escalar de un vector por sí mismo es igual a su módulo al :@0.108233:0.726092:0.599917:0.726092:0.599917:0.709594:0.108233:0.709594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadrado, ya que el coseno de cero es uno.:@0.108233:0.743443:0.411366:0.743443:0.411366:0.726945:0.108233:0.726945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅=:@0.122054:0.768144:0.151587:0.768144:0.151587:0.751863:0.122054:0.751863:0.000000:0.000000
=:@0.216077:0.768144:0.226653:0.768144:0.226653:0.751863:0.216077:0.751863:0.000000
⋅:@0.254453:0.768144:0.259269:0.768144:0.259269:0.751863:0.254453:0.751863:0.000000
vv:@0.110641:0.767623:0.135763:0.767623:0.135763:0.751154:0.110641:0.751154:0.000000:0.000000
v:@0.160577:0.767623:0.168360:0.767623:0.168360:0.751154:0.160577:0.751154:0.000000
v:@0.197373:0.767623:0.205157:0.767623:0.205157:0.751154:0.197373:0.751154:0.000000
vv:@0.243038:0.767623:0.268160:0.767623:0.268160:0.751154:0.243038:0.751154:0.000000:0.000000
;:@0.185452:0.767507:0.188206:0.767507:0.188206:0.751010:0.185452:0.751010:0.000000
2:@0.176290:0.757349:0.181207:0.757349:0.181207:0.747801:0.176290:0.747801:0.000000
.:@0.272299:0.766250:0.275054:0.766250:0.275054:0.749752:0.272299:0.749752:0.000000
Definición:@0.108236:0.799997:0.188320:0.799997:0.188320:0.783051:0.108236:0.783051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,     de :@0.108236:0.824014:0.231024:0.824009:0.231024:0.807512:0.108236:0.807516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.149725:0.824125:0.178705:0.824125:0.178705:0.807656:0.149725:0.807656:0.000000:0.000000:0.000000
:@0.187292:0.823792:0.203340:0.823792:0.203340:0.809145:0.187292:0.809145:0.000000
V:@0.232565:0.824125:0.243315:0.824125:0.243315:0.807656:0.232565:0.807656:0.000000
2 :@0.243334:0.826680:0.250062:0.826680:0.250062:0.817899:0.243334:0.817899:0.000000:0.000000
. Se dice que   y   son ortogonales si y solo si :@0.250885:0.824009:0.599870:0.824009:0.599870:0.807512:0.250885:0.807512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.351250:0.824125:0.360459:0.824125:0.360459:0.807656:0.351250:0.807656:0.000000
v:@0.383204:0.824125:0.390987:0.824125:0.390987:0.807656:0.383204:0.807656:0.000000
forman un ángulo recto. Escribiremos :@0.108225:0.841360:0.378647:0.841360:0.378647:0.824862:0.108225:0.824862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.496108:0.841360:0.504604:0.841360:0.504604:0.824862:0.496108:0.824862:0.000000
⊥:@0.393386:0.841996:0.406062:0.841996:0.406062:0.825715:0.393386:0.825715:0.000000
→ ⋅=:@0.425732:0.841996:0.492178:0.841996:0.492178:0.825715:0.425732:0.825715:0.000000:0.000000:0.000000:0.000000
u:@0.379939:0.841476:0.389147:0.841476:0.389147:0.825007:0.379939:0.825007:0.000000
v:@0.409723:0.841476:0.417506:0.841476:0.417506:0.825007:0.409723:0.825007:0.000000
uv:@0.450815:0.841476:0.476342:0.841476:0.476342:0.825007:0.450815:0.825007:0.000000:0.000000
.:@0.419970:0.841360:0.422725:0.841360:0.422725:0.824862:0.419970:0.824862:0.000000
En la figura 2.25. se muestran dos vecto-:@0.108239:0.862268:0.396116:0.862268:0.396116:0.845770:0.108239:0.845770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
res ortogonales.:@0.108239:0.879618:0.219708:0.879618:0.219708:0.863121:0.108239:0.863121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El producto escalar entre dos vectores :@0.108239:0.900526:0.400300:0.900526:0.400300:0.884028:0.108239:0.884028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ortogonales es nulo. Se tiene :@0.108239:0.917877:0.325761:0.917877:0.325761:0.901379:0.108239:0.901379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.446745:0.917891:0.455241:0.917891:0.455241:0.901393:0.446745:0.901393:0.000000
⊥:@0.344023:0.918527:0.356700:0.918527:0.356700:0.902246:0.344023:0.902246:0.000000
→ ⋅=:@0.376369:0.918527:0.442815:0.918527:0.442815:0.902246:0.376369:0.902246:0.000000:0.000000:0.000000:0.000000
u:@0.330576:0.918006:0.339785:0.918006:0.339785:0.901537:0.330576:0.901537:0.000000
v:@0.360360:0.918006:0.368143:0.918006:0.368143:0.901537:0.360360:0.901537:0.000000
uv:@0.401453:0.918006:0.426979:0.918006:0.426979:0.901537:0.401453:0.901537:0.000000:0.000000
 :@0.371604:0.917891:0.375746:0.917891:0.375746:0.901393:0.371604:0.901393:0.000000
 :@0.396162:0.917891:0.400304:0.917891:0.400304:0.901393:0.396162:0.901393:0.000000
0 .:@0.156132:0.935241:0.171241:0.935241:0.171241:0.918744:0.156132:0.918744:0.000000:0.000000:0.000000
⊥:@0.053409:0.935878:0.066086:0.935878:0.066086:0.919597:0.053409:0.919597:0.000000
→ ⋅=:@0.085756:0.935878:0.152201:0.935878:0.152201:0.919597:0.085756:0.919597:0.000000:0.000000:0.000000:0.000000
u:@0.039962:0.935357:0.049171:0.935357:0.049171:0.918888:0.039962:0.918888:0.000000
v:@0.069746:0.935357:0.077529:0.935357:0.077529:0.918888:0.069746:0.918888:0.000000
uv:@0.110839:0.935357:0.136365:0.935357:0.136365:0.918888:0.110839:0.918888:0.000000:0.000000
v:@0.789722:0.319984:0.796027:0.319984:0.796027:0.306645:0.789722:0.306645:0.000000
p:@0.787313:0.360183:0.798794:0.360183:0.798794:0.350158:0.787313:0.350158:0.000000
 :@0.798794:0.360891:0.801675:0.360891:0.801675:0.349414:0.798794:0.349414:0.000000
Figura 2.23.:@0.801675:0.360891:0.856154:0.360891:0.856154:0.349414:0.801675:0.349414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.671685:0.322720:0.679973:0.322720:0.679973:0.307898:0.671685:0.307898:0.000000
120°:@0.429824:0.555905:0.457897:0.555905:0.457897:0.540842:0.429824:0.540842:0.000000:0.000000:0.000000:0.000000
x:@0.498053:0.539002:0.503318:0.539002:0.503318:0.527402:0.498053:0.527402:0.000000
 = –3:@0.503318:0.538920:0.530145:0.538920:0.530145:0.527300:0.503318:0.527300:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.549250:0.623540:0.555235:0.623540:0.555235:0.611920:0.549250:0.611920:0.000000
a:@0.425879:0.582997:0.433958:0.582997:0.433958:0.568175:0.425879:0.568175:0.000000
p:@0.526926:0.641051:0.538406:0.641051:0.538406:0.631027:0.526926:0.631027:0.000000
 :@0.538406:0.641759:0.541288:0.641759:0.541288:0.630282:0.538406:0.630282:0.000000
Figura 2.24.:@0.541288:0.641759:0.595766:0.641759:0.595766:0.630282:0.541288:0.630282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.541969:0.905630:0.550257:0.905630:0.550257:0.890808:0.541969:0.890808:0.000000
v:@0.431085:0.896007:0.438090:0.896007:0.438090:0.881185:0.431085:0.881185:0.000000
p:@0.526926:0.940784:0.538406:0.940784:0.538406:0.930759:0.526926:0.930759:0.000000
 Figura 2.25.:@0.538406:0.941492:0.595766:0.941492:0.595766:0.930015:0.538406:0.930015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.549634:0.564226:0.555048:0.564226:0.555048:0.552626:0.549634:0.552626:0.000000
 = 3    3:@0.555048:0.564144:0.592133:0.564144:0.592133:0.552524:0.555048:0.552524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.684010:0.104916:0.781633:0.104916:0.781633:0.089444:0.684010:0.089444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684010:0.117484:0.768072:0.117484:0.768072:0.102012:0.684010:0.102012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Podemos multiplicar un :@0.684246:0.141959:0.837156:0.141959:0.837156:0.126896:0.684246:0.126896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector por un escalar (número)  :@0.637703:0.157801:0.838387:0.157801:0.838387:0.142738:0.637703:0.142738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y el resultado será otro vector.:@0.637703:0.173643:0.820883:0.173643:0.820883:0.158580:0.637703:0.158580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Practica :@0.637703:0.200600:0.698721:0.200600:0.698721:0.185128:0.637703:0.185128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en tu cuaderno.:@0.698721:0.200178:0.800600:0.200178:0.800600:0.185115:0.698721:0.185115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dado :@0.637703:0.223835:0.677632:0.223835:0.677632:0.208772:0.637703:0.208772:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.734590:0.224048:0.745531:0.224048:0.749826:0.209395:0.738886:0.209395:0.000000
=:@0.701667:0.224048:0.711185:0.224048:0.711185:0.209395:0.701667:0.209395:0.000000
=:@0.750579:0.224048:0.760098:0.224048:0.760098:0.209395:0.750579:0.209395:0.000000
a:@0.685412:0.223580:0.693492:0.223580:0.693492:0.208758:0.685412:0.208758:0.000000
4y:@0.714003:0.223475:0.732642:0.223475:0.732642:0.208628:0.714003:0.208628:0.000000:0.000000
5:@0.762153:0.223475:0.769799:0.223475:0.769799:0.208628:0.762153:0.208628:0.000000
, :@0.772623:0.223837:0.778920:0.223837:0.778920:0.208774:0.772623:0.208774:0.000000:0.000000
calcula  :@0.778920:0.224259:0.835435:0.224259:0.835435:0.208787:0.778920:0.208787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
||:@0.637708:0.239679:0.645975:0.239679:0.645975:0.224616:0.637708:0.224616:0.000000:0.000000
α:@0.643223:0.240635:0.655380:0.240635:0.660152:0.224355:0.647996:0.224355:0.000000
a:@0.658363:0.240115:0.667341:0.240115:0.667341:0.223646:0.658363:0.223646:0.000000
||:@0.668259:0.239679:0.676526:0.239679:0.676526:0.224616:0.668259:0.224616:0.000000:0.000000
.:@0.675647:0.240101:0.679323:0.240101:0.679323:0.224629:0.675647:0.224629:0.000000
Competencia :@0.684010:0.638698:0.781633:0.638698:0.781633:0.623226:0.684010:0.623226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684010:0.651266:0.768072:0.651266:0.768072:0.635794:0.684010:0.635794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ley de senos para :@0.684246:0.675741:0.817348:0.675741:0.817348:0.660678:0.684246:0.660678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
triángulos oblicuángulos  :@0.637703:0.691583:0.803663:0.691583:0.803663:0.676520:0.637703:0.676520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
establece que::@0.637703:0.707425:0.728817:0.707425:0.728817:0.692362:0.637703:0.692362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.686295:0.813936:0.694291:0.813936:0.694291:0.799267:0.686295:0.799267:0.000000
b:@0.738049:0.813936:0.746303:0.813936:0.746303:0.799267:0.738049:0.799267:0.000000
c:@0.790181:0.813936:0.796582:0.813936:0.796582:0.799267:0.790181:0.799267:0.000000
sen:@0.673047:0.831967:0.694119:0.831967:0.694119:0.817272:0.673047:0.817272:0.000000:0.000000:0.000000
sen:@0.725505:0.831967:0.746578:0.831967:0.746578:0.817272:0.725505:0.817272:0.000000:0.000000:0.000000
sen:@0.777260:0.831967:0.798332:0.831967:0.798332:0.817272:0.777260:0.817272:0.000000:0.000000:0.000000
α:@0.693093:0.832529:0.703921:0.832529:0.708172:0.818027:0.697344:0.818027:0.000000
β:@0.746632:0.832529:0.756053:0.832529:0.760304:0.818027:0.750883:0.818027:0.000000
γ:@0.797323:0.832529:0.804376:0.832529:0.808626:0.818027:0.801574:0.818027:0.000000
=:@0.711475:0.822730:0.720896:0.822730:0.720896:0.808228:0.711475:0.808228:0.000000
=:@0.763230:0.822730:0.772651:0.822730:0.772651:0.808228:0.763230:0.808228:0.000000
B:@0.666760:0.789759:0.675030:0.789759:0.675030:0.774937:0.666760:0.774937:0.000000
c:@0.680960:0.756081:0.687427:0.756081:0.687427:0.741259:0.680960:0.741259:0.000000
b:@0.759574:0.755365:0.767914:0.755365:0.767914:0.740543:0.759574:0.740543:0.000000
a:@0.729543:0.793142:0.737623:0.793142:0.737623:0.778320:0.729543:0.778320:0.000000
A:@0.697189:0.727400:0.707332:0.727400:0.707332:0.712578:0.697189:0.712578:0.000000
C:@0.807775:0.789759:0.816809:0.789759:0.816809:0.774937:0.807775:0.774937:0.000000
La ley de cosenos establece que::@0.637709:0.861279:0.845425:0.861279:0.845425:0.846216:0.637709:0.846216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.658110:0.887053:0.668043:0.887053:0.668043:0.871763:0.658110:0.871763:0.000000
+ −:@0.687457:0.887053:0.725053:0.887053:0.725053:0.871763:0.687457:0.871763:0.000000:0.000000:0.000000
β:@0.778119:0.887053:0.788052:0.887053:0.788052:0.871763:0.778119:0.871763:0.000000
=:@0.658110:0.909083:0.668043:0.909083:0.668043:0.893793:0.658110:0.893793:0.000000
+ −:@0.687457:0.909083:0.725053:0.909083:0.725053:0.893793:0.687457:0.893793:0.000000:0.000000:0.000000
α:@0.778499:0.909083:0.789915:0.909083:0.789915:0.893793:0.778499:0.893793:0.000000
=:@0.656980:0.931113:0.666912:0.931113:0.666912:0.915823:0.656980:0.915823:0.000000
+:@0.686326:0.931113:0.696259:0.931113:0.696259:0.915823:0.686326:0.915823:0.000000
−:@0.715120:0.931113:0.725053:0.931113:0.725053:0.915823:0.715120:0.915823:0.000000
δ:@0.780000:0.931113:0.788938:0.931113:0.788938:0.915823:0.780000:0.915823:0.000000
b:@0.639971:0.886564:0.648673:0.886564:0.648673:0.871097:0.639971:0.871097:0.000000
a:@0.671018:0.886564:0.679449:0.886564:0.679449:0.871097:0.671018:0.871097:0.000000
c:@0.699423:0.886564:0.706172:0.886564:0.706172:0.871097:0.699423:0.871097:0.000000
ac:@0.735283:0.886564:0.750318:0.886564:0.750318:0.871097:0.735283:0.871097:0.000000:0.000000
a:@0.640333:0.908589:0.648764:0.908589:0.648764:0.893122:0.640333:0.893122:0.000000
b:@0.670638:0.908589:0.679340:0.908589:0.679340:0.893122:0.670638:0.893122:0.000000
c:@0.699423:0.908589:0.706172:0.908589:0.706172:0.893122:0.699423:0.893122:0.000000
bc:@0.734903:0.908589:0.750318:0.908589:0.750318:0.893122:0.734903:0.893122:0.000000:0.000000
c:@0.640333:0.930613:0.647081:0.930613:0.647081:0.915147:0.640333:0.915147:0.000000
a:@0.669878:0.930613:0.678309:0.930613:0.678309:0.915147:0.669878:0.915147:0.000000
b:@0.697903:0.930613:0.706606:0.930613:0.706606:0.915147:0.697903:0.915147:0.000000
ab:@0.735265:0.930613:0.752253:0.930613:0.752253:0.915147:0.735265:0.915147:0.000000:0.000000
2cos().:@0.726689:0.886441:0.795308:0.886455:0.795308:0.870962:0.726689:0.870948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2cos().:@0.726719:0.908480:0.797570:0.908485:0.797570:0.892992:0.726719:0.892986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.726719:0.930510:0.734698:0.930510:0.734698:0.915017:0.726719:0.915017:0.000000
cos().:@0.753333:0.930510:0.796439:0.930516:0.796439:0.915022:0.753333:0.915017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.648875:0.878913:0.653488:0.878913:0.653488:0.869956:0.648875:0.869956:0.000000
2:@0.679543:0.878913:0.684155:0.878913:0.684155:0.869956:0.679543:0.869956:0.000000
2:@0.706832:0.878913:0.711445:0.878913:0.711445:0.869956:0.706832:0.869956:0.000000
2:@0.648875:0.900940:0.653488:0.900940:0.653488:0.891983:0.648875:0.891983:0.000000
2:@0.679543:0.900940:0.684155:0.900940:0.684155:0.891983:0.679543:0.891983:0.000000
2:@0.706832:0.900940:0.711445:0.900940:0.711445:0.891983:0.706832:0.891983:0.000000
2:@0.647745:0.922968:0.652358:0.922968:0.652358:0.914011:0.647745:0.914011:0.000000
2:@0.678413:0.922968:0.683026:0.922968:0.683026:0.914011:0.678413:0.914011:0.000000
2:@0.706832:0.922968:0.711445:0.922968:0.711445:0.914011:0.706832:0.914011:0.000000
Competencia :@0.684804:0.401749:0.782426:0.401749:0.782426:0.386276:0.684804:0.386276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.684804:0.414317:0.796762:0.414317:0.796762:0.398844:0.684804:0.398844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la siguiente :@0.678232:0.438791:0.814697:0.438791:0.814697:0.423728:0.678232:0.423728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simbología matemática::@0.638496:0.454633:0.793269:0.454633:0.793269:0.439570:0.638496:0.439570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• Al producto escalar de dos :@0.638496:0.474040:0.825527:0.474040:0.825527:0.458976:0.638496:0.458976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectores, lo representamos por :@0.638496:0.489882:0.842396:0.489882:0.842396:0.474818:0.638496:0.474818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el punto entre los vectores::@0.638496:0.507229:0.813620:0.507229:0.813620:0.492165:0.638496:0.492165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.813628:0.507552:0.817770:0.507552:0.817770:0.491054:0.813628:0.491054:0.000000
⋅:@0.655098:0.524030:0.659915:0.524030:0.659915:0.507749:0.655098:0.507749:0.000000
uv:@0.643268:0.523509:0.668794:0.523509:0.668794:0.507041:0.643268:0.507041:0.000000:0.000000
.:@0.670479:0.523073:0.672994:0.523073:0.672994:0.508010:0.670479:0.508010:0.000000
• Al producto por un escalar, :@0.638500:0.542479:0.827994:0.542479:0.827994:0.527416:0.638500:0.527416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llamado también multiplicación :@0.638500:0.558321:0.850423:0.558321:0.850423:0.543258:0.638500:0.543258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de un vector por un escalar, lo :@0.638500:0.574163:0.838565:0.574163:0.838565:0.559100:0.638500:0.559100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representamos sin el punto::@0.638500:0.591510:0.817600:0.591510:0.817600:0.576447:0.638500:0.576447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.818115:0.592471:0.830271:0.592471:0.835044:0.576190:0.822887:0.576190:0.000000
u:@0.832417:0.591951:0.841626:0.591951:0.841626:0.575482:0.832417:0.575482:0.000000
.:@0.843404:0.591835:0.846159:0.591835:0.846159:0.575337:0.843404:0.575337:0.000000
 ©:@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
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