151:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, métrico, numérico y variacional:@0.444620:0.043661:0.926912:0.043661:0.926912:0.024916:0.444620:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.5 Producto escalar o producto punto de dos vectores:@0.073089:0.136363:0.501652:0.136363:0.501652:0.119417:0.073089:0.119417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.073089:0.163018:0.151058:0.163018:0.151058:0.146349:0.073089:0.146349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,     de  . Se define el producto escalar de   con  , que se denota :@0.073089:0.190380:0.626888:0.190375:0.626888:0.173941:0.073089:0.173946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.113732:0.190380:0.138748:0.190380:0.138748:0.173974:0.113732:0.173974:0.000000:0.000000:0.000000
[:@0.143478:0.190241:0.158811:0.190241:0.158811:0.176193:0.143478:0.176193:0.000000
V:@0.187287:0.190380:0.196399:0.190380:0.196399:0.173974:0.187287:0.173974:0.000000
2:@0.196438:0.193547:0.201675:0.193547:0.201675:0.183966:0.196438:0.183966:0.000000
u:@0.453510:0.190375:0.462824:0.190375:0.462824:0.173969:0.453510:0.173969:0.000000
v:@0.500246:0.190375:0.507977:0.190375:0.507977:0.173969:0.500246:0.173969:0.000000
u   v:@0.627625:0.190375:0.658622:0.190375:0.658622:0.173969:0.627625:0.173969:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.640841:0.190236:0.646971:0.190236:0.646971:0.176188:0.640841:0.176188:0.000000
 como  :@0.658659:0.190375:0.710384:0.190375:0.710384:0.173941:0.658659:0.173941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u   v:@0.073106:0.207017:0.102613:0.207017:0.102613:0.190611:0.073106:0.190611:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.085605:0.206878:0.091734:0.206878:0.091734:0.192830:0.085605:0.192830:0.000000
5:@0.102539:0.206462:0.117873:0.206462:0.117873:0.192746:0.102539:0.192746:0.000000
ІІ ІІ ІІ ІІ:@0.117780:0.207017:0.168419:0.207017:0.168419:0.190583:0.117780:0.190583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u   v cos:@0.125383:0.207017:0.191251:0.207017:0.191251:0.190611:0.125383:0.190611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ), donde   :@0.191189:0.207017:0.282286:0.207017:0.282286:0.190583:0.191189:0.190583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.195993:0.206462:0.205197:0.206462:0.205197:0.192746:0.195993:0.192746:0.000000
u:@0.269143:0.206462:0.278347:0.206462:0.278347:0.192746:0.269143:0.192746:0.000000
[:@0.282212:0.206878:0.297546:0.206878:0.297546:0.192830:0.282212:0.192830:0.000000
3:@0.297454:0.207599:0.301540:0.207599:0.301540:0.189945:0.297454:0.189945:0.000000
0,   es el ángulo que forman los vectores   y  .:@0.301448:0.207017:0.643510:0.207017:0.643510:0.190583:0.301448:0.190583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.317426:0.206462:0.329703:0.206462:0.329703:0.192746:0.317426:0.192746:0.000000
4:@0.329611:0.207599:0.333698:0.207599:0.333698:0.189945:0.329611:0.189945:0.000000
u v:@0.607487:0.207017:0.640381:0.207017:0.640381:0.190611:0.607487:0.190611:0.000000:0.000000:0.000000
Para el caso particular :@0.073069:0.234379:0.234008:0.234379:0.234008:0.217945:0.073069:0.217945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u   v:@0.233783:0.234379:0.272493:0.234379:0.272493:0.217973:0.233783:0.217973:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.246282:0.233824:0.261615:0.233824:0.261615:0.220108:0.246282:0.220108:0.000000
, se obtiene ІІ ІІ    :@0.272420:0.234379:0.411334:0.234380:0.411334:0.217946:0.272420:0.217945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.367272:0.234379:0.376586:0.234379:0.376586:0.217973:0.367272:0.217973:0.000000
5:@0.388073:0.233824:0.403406:0.233824:0.403406:0.220108:0.388073:0.220108:0.000000
u u:@0.416426:0.234380:0.441019:0.234380:0.441019:0.217974:0.416426:0.217974:0.000000:0.000000:0.000000
?:@0.425667:0.234241:0.431797:0.234241:0.431797:0.220193:0.425667:0.220193:0.000000
.:@0.440945:0.234380:0.444148:0.234380:0.444148:0.217946:0.440945:0.217946:0.000000
El espacio vectorial   provisto del producto escalar se llama :@0.073076:0.261742:0.510706:0.261743:0.510706:0.245309:0.073076:0.245308:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.214628:0.261742:0.223739:0.261742:0.223739:0.245336:0.214628:0.245336:0.000000
2:@0.223686:0.264916:0.228923:0.264916:0.228923:0.255335:0.223686:0.255335:0.000000
espacio euclídeo :@0.510397:0.261743:0.641512:0.261743:0.641512:0.245074:0.510397:0.245074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.641365:0.261743:0.650476:0.261743:0.650476:0.245337:0.641365:0.245337:0.000000
2:@0.650404:0.264916:0.655641:0.264916:0.655641:0.255335:0.650404:0.255335:0.000000
 .:@0.655595:0.261743:0.662756:0.261743:0.662756:0.245309:0.655595:0.245309:0.000000:0.000000
Ejercicio resuelto:@0.073098:0.289105:0.201676:0.289105:0.201676:0.272436:0.073098:0.272436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dados los vectores  ,   :@0.073098:0.316467:0.248353:0.316467:0.248353:0.300033:0.073098:0.300033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.218865:0.316467:0.244248:0.316467:0.244248:0.300061:0.218865:0.300061:0.000000:0.000000:0.000000
[:@0.249292:0.316328:0.264625:0.316328:0.264625:0.302280:0.249292:0.302280:0.000000
V:@0.264736:0.316467:0.273847:0.316467:0.273847:0.300061:0.264736:0.300061:0.000000
2:@0.273916:0.319642:0.279153:0.319642:0.279153:0.310061:0.273916:0.310061:0.000000
, donde ІІ ІІ 2, ІІ ІІ 1,   es un :@0.279205:0.316470:0.513511:0.316470:0.513511:0.300036:0.279205:0.300036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.349447:0.316470:0.358762:0.316470:0.358762:0.300064:0.349447:0.300064:0.000000
5:@0.366787:0.315915:0.382120:0.315915:0.382120:0.302199:0.366787:0.302199:0.000000
v:@0.407504:0.316470:0.415235:0.316470:0.415235:0.300064:0.407504:0.300064:0.000000
5:@0.423261:0.315915:0.438594:0.315915:0.438594:0.302199:0.423261:0.302199:0.000000
v:@0.456025:0.316470:0.463757:0.316470:0.463757:0.300064:0.456025:0.300064:0.000000
vector horizontal y   forma un ángulo de 120° respecto de la :@0.073081:0.333112:0.513679:0.333112:0.513679:0.316678:0.073081:0.316678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.211393:0.333112:0.220707:0.333112:0.220707:0.316705:0.211393:0.316705:0.000000
horizontal y en el sentido antihorario (véase Figura 2.10.), :@0.073063:0.349753:0.513158:0.349753:0.513158:0.333320:0.073063:0.333320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
calcula la norma y determina el ángulo que forma el vector :@0.073063:0.366395:0.513250:0.366395:0.513250:0.349961:0.073063:0.349961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resultante respecto de la horizontal y en el sentido antihorario :@0.073063:0.383037:0.513587:0.383037:0.513587:0.366603:0.073063:0.366603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para :@0.073063:0.399679:0.109104:0.399679:0.109104:0.383245:0.073063:0.383245:0.000000:0.000000:0.000000:0.000000:0.000000
a5 2:@0.108994:0.399124:0.168872:0.399124:0.168872:0.385408:0.108994:0.385408:0.000000:0.000000:0.000000:0.000000
3:@0.135390:0.399679:0.144372:0.399679:0.144372:0.383245:0.135390:0.383245:0.000000
u:@0.144299:0.399679:0.153613:0.399679:0.153613:0.383273:0.144299:0.383273:0.000000
2 .:@0.168780:0.399679:0.188550:0.399679:0.188550:0.383245:0.168780:0.383245:0.000000:0.000000:0.000000
v:@0.177689:0.399679:0.185420:0.399679:0.185420:0.383273:0.177689:0.383273:0.000000
ІІ ІІ :@0.073063:0.427041:0.101502:0.427041:0.101502:0.410607:0.073063:0.410607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.080665:0.427041:0.089924:0.427041:0.089924:0.410635:0.080665:0.410635:0.000000
5  :@0.101445:0.426487:0.125798:0.426487:0.125798:0.412772:0.101445:0.412772:0.000000:0.000000:0.000000
5    (3  3)2   2  13:@0.130308:0.427042:0.272033:0.427042:0.272033:0.410608:0.130308:0.410608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.139210:0.420978:0.144447:0.420978:0.144447:0.411397:0.139210:0.411397:0.000000
1:@0.148357:0.426487:0.163690:0.426487:0.163690:0.412772:0.148357:0.412772:0.000000
5:@0.216917:0.426487:0.232250:0.426487:0.232250:0.412772:0.216917:0.412772:0.000000
Se tiene ІІ3 ІІ 3ІІ ІІ 6, ІІ2 ІІ 2ІІ ІІ 2.:@0.073089:0.454405:0.354536:0.454405:0.354536:0.437971:0.073089:0.437971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.151743:0.454405:0.161057:0.454405:0.161057:0.437999:0.151743:0.437999:0.000000
5:@0.168586:0.453851:0.183919:0.453851:0.183919:0.440135:0.168586:0.440135:0.000000
u:@0.200338:0.454405:0.209652:0.454405:0.209652:0.437999:0.200338:0.437999:0.000000
5:@0.217181:0.453851:0.232514:0.453851:0.232514:0.440135:0.217181:0.440135:0.000000
v:@0.264911:0.454405:0.272642:0.454405:0.272642:0.437999:0.264911:0.437999:0.000000
5:@0.280170:0.453851:0.295504:0.453851:0.295504:0.440135:0.280170:0.440135:0.000000
v:@0.311923:0.454405:0.319654:0.454405:0.319654:0.437999:0.311923:0.437999:0.000000
5:@0.327182:0.453851:0.342516:0.453851:0.342516:0.440135:0.327182:0.440135:0.000000
Ángulo que forman los vectores 3  y  2 : 120º.:@0.073052:0.481767:0.418206:0.481767:0.418206:0.465333:0.073052:0.465333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.318089:0.481767:0.327403:0.481767:0.327403:0.465361:0.318089:0.465361:0.000000
2:@0.343252:0.481213:0.358585:0.481213:0.358585:0.467497:0.343252:0.467497:0.000000
v:@0.367402:0.481767:0.375133:0.481767:0.375133:0.465361:0.367402:0.465361:0.000000
Por la ley de los cosenos::@0.073052:0.509129:0.251626:0.509129:0.251626:0.492695:0.073052:0.492695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ІІ ІІ:@0.073052:0.536491:0.097534:0.536491:0.097534:0.520057:0.073052:0.520057:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.080654:0.536491:0.089913:0.536491:0.089913:0.520085:0.080654:0.520085:0.000000
2:@0.097495:0.530430:0.102731:0.530430:0.102731:0.520849:0.097495:0.520849:0.000000
5:@0.102684:0.535939:0.118018:0.535939:0.118018:0.522223:0.102684:0.522223:0.000000
ІІ3 ІІ:@0.117926:0.536494:0.151372:0.536494:0.151372:0.520060:0.117926:0.520060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.134437:0.536494:0.143751:0.536494:0.143751:0.520088:0.134437:0.520088:0.000000
2:@0.151288:0.530430:0.156525:0.530430:0.156525:0.520849:0.151288:0.520849:0.000000
1 2:@0.156479:0.535939:0.194656:0.535939:0.194656:0.522223:0.156479:0.522223:0.000000:0.000000:0.000000
ІІ 2 ІІ:@0.171720:0.536494:0.218825:0.536494:0.218825:0.520060:0.171720:0.520060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.203473:0.536494:0.211204:0.536494:0.211204:0.520088:0.203473:0.520088:0.000000
2:@0.218741:0.530430:0.223978:0.530430:0.223978:0.520849:0.218741:0.520849:0.000000
2:@0.223932:0.535939:0.239265:0.535939:0.239265:0.522223:0.223932:0.522223:0.000000
2ІІ3 ІІІ 2 ІІ :@0.239173:0.536494:0.328687:0.536494:0.328687:0.520060:0.239173:0.520060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.264575:0.536494:0.273889:0.536494:0.273889:0.520088:0.264575:0.520088:0.000000
2:@0.285228:0.535939:0.300561:0.535939:0.300561:0.522223:0.285228:0.522223:0.000000
v cos:@0.309378:0.536494:0.351520:0.536494:0.351520:0.520088:0.309378:0.520088:0.000000:0.000000:0.000000:0.000000:0.000000
(120°):@0.351457:0.536494:0.393205:0.536494:0.393205:0.520060:0.351457:0.520060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ІІ ІІ 2  13:@0.073066:0.563856:0.148660:0.563857:0.148660:0.547423:0.073066:0.547422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.080668:0.563856:0.089927:0.563856:0.089927:0.547450:0.080668:0.547450:0.000000
5:@0.097456:0.563301:0.112789:0.563301:0.112789:0.549585:0.097456:0.549585:0.000000
Por la ley de senos: :@0.073089:0.591220:0.213542:0.591220:0.213542:0.574786:0.073089:0.574786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2  13:@0.092014:0.616909:0.127945:0.616909:0.127945:0.600475:0.092014:0.600475:0.000000:0.000000:0.000000:0.000000:0.000000
sen:@0.077385:0.630884:0.100891:0.630884:0.100891:0.614478:0.077385:0.614478:0.000000:0.000000:0.000000
(120°):@0.100836:0.630884:0.142584:0.630884:0.142584:0.614451:0.100836:0.614451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.146769:0.622967:0.169999:0.622967:0.169999:0.606533:0.146769:0.606533:0.000000:0.000000:0.000000
5:@0.150726:0.622412:0.166059:0.622412:0.166059:0.608697:0.150726:0.608697:0.000000
2:@0.192785:0.616904:0.201768:0.616904:0.201768:0.600470:0.192785:0.600470:0.000000
sen:@0.175132:0.630883:0.198639:0.630883:0.198639:0.614477:0.175132:0.614477:0.000000:0.000000:0.000000
( ):@0.198583:0.630883:0.219420:0.630883:0.219420:0.614449:0.198583:0.614449:0.000000:0.000000:0.000000
a:@0.203388:0.630328:0.214634:0.630328:0.214634:0.616613:0.203388:0.616613:0.000000
sen:@0.073083:0.654903:0.096589:0.654903:0.096589:0.638497:0.073083:0.638497:0.000000:0.000000:0.000000
( )   :@0.096533:0.654903:0.140508:0.654903:0.140508:0.638469:0.096533:0.638469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a 5:@0.101338:0.654348:0.136569:0.654348:0.136569:0.640632:0.101338:0.640632:0.000000:0.000000:0.000000
2:@0.144200:0.649543:0.153183:0.649543:0.153183:0.633110:0.144200:0.633110:0.000000
sen:@0.153109:0.649543:0.176615:0.649543:0.176615:0.633137:0.153109:0.633137:0.000000:0.000000:0.000000
(120°):@0.176560:0.649543:0.218308:0.649543:0.218308:0.633110:0.176560:0.633110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2  13:@0.163280:0.663517:0.199211:0.663517:0.199211:0.647084:0.163280:0.647084:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.221952:0.654891:0.245182:0.654891:0.245182:0.638458:0.221952:0.638458:0.000000:0.000000:0.000000
5:@0.225910:0.654337:0.241243:0.654337:0.241243:0.640621:0.225910:0.640621:0.000000
  39:@0.254958:0.648650:0.281980:0.648650:0.281980:0.632216:0.254958:0.632216:0.000000:0.000000:0.000000:0.000000
26:@0.259520:0.662624:0.277412:0.662624:0.277412:0.646190:0.259520:0.646190:0.000000:0.000000
a 5:@0.073089:0.681700:0.103534:0.681700:0.103534:0.667984:0.073089:0.667984:0.000000:0.000000:0.000000
   13,89788625.:@0.084243:0.682255:0.202823:0.682255:0.202823:0.665821:0.084243:0.665821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El ángulo del vector resultante es:     13,9°   120°   133,9°, medido en sentido :@0.073089:0.709617:0.710403:0.709617:0.710403:0.693183:0.073089:0.693183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V 5:@0.339578:0.709062:0.375225:0.709062:0.375225:0.695346:0.339578:0.695346:0.000000:0.000000:0.000000
1:@0.423636:0.709062:0.438970:0.709062:0.438970:0.695346:0.423636:0.695346:0.000000
5:@0.483957:0.709062:0.499290:0.709062:0.499290:0.695346:0.483957:0.695346:0.000000
antihorario.:@0.073107:0.726258:0.155559:0.726258:0.155559:0.709825:0.073107:0.709825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El producto escalar de un vector por sí mismo es igual a su módulo al cuadrado, ya que :@0.073107:0.753620:0.710928:0.753620:0.710928:0.737187:0.073107:0.737187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el coseno de cero es uno.:@0.073107:0.770262:0.256962:0.770262:0.256962:0.753828:0.073107:0.753828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v v:@0.073107:0.797624:0.102448:0.797624:0.102448:0.781218:0.073107:0.781218:0.000000:0.000000:0.000000
       ІІ ІІ ; ІІ ІІ:@0.080765:0.797624:0.183590:0.797627:0.183590:0.781193:0.080765:0.781190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.084722:0.797486:0.090852:0.797486:0.090852:0.783437:0.084722:0.783437:0.000000
5:@0.106332:0.797069:0.121665:0.797069:0.121665:0.783354:0.106332:0.783354:0.000000
v:@0.133133:0.797624:0.140864:0.797624:0.140864:0.781218:0.133133:0.781218:0.000000
2:@0.148377:0.791563:0.153614:0.791563:0.153614:0.781982:0.148377:0.781982:0.000000
v      v   v.:@0.168238:0.797627:0.244909:0.797627:0.244909:0.781221:0.168238:0.781221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.186737:0.797072:0.202071:0.797072:0.202071:0.783356:0.186737:0.783356:0.000000
?:@0.225306:0.797488:0.231435:0.797488:0.231435:0.783440:0.225306:0.783440:0.000000
Definición:@0.073078:0.824989:0.147454:0.824989:0.147454:0.808555:0.073078:0.808555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,     de   . Se dice que   y   son ortogonales si y solo :@0.073078:0.852351:0.510781:0.852353:0.510781:0.835919:0.073078:0.835917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.112211:0.852351:0.135975:0.852351:0.135975:0.835945:0.112211:0.835945:0.000000:0.000000:0.000000
[:@0.139565:0.852212:0.154898:0.852212:0.154898:0.838163:0.139565:0.838163:0.000000
V:@0.180926:0.852351:0.190037:0.852351:0.190037:0.835945:0.180926:0.835945:0.000000
2:@0.189992:0.855525:0.195229:0.855525:0.195229:0.845945:0.189992:0.845945:0.000000
u v:@0.293165:0.852353:0.325488:0.852353:0.325488:0.835947:0.293165:0.835947:0.000000:0.000000:0.000000
si forman un ángulo recto. Escribiremos :@0.073088:0.868995:0.363368:0.868995:0.363368:0.852561:0.073088:0.852561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u   v:@0.363076:0.868995:0.401786:0.868995:0.401786:0.852589:0.363076:0.852589:0.000000:0.000000:0.000000:0.000000:0.000000
':@0.375574:0.868135:0.390907:0.868135:0.390907:0.855238:0.375574:0.855238:0.000000
.:@0.401712:0.868995:0.404915:0.868995:0.404915:0.852561:0.401712:0.852561:0.000000
En la Figura 2.12. se muestran dos vectores ortogonales.:@0.073088:0.896357:0.476829:0.896357:0.476829:0.879923:0.073088:0.879923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El producto escalar entre dos vectores ortogonales es nulo. :@0.073088:0.923719:0.510774:0.923719:0.510774:0.907285:0.073088:0.907285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se tiene :@0.073088:0.940361:0.135370:0.940361:0.135370:0.923927:0.073088:0.923927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u   v:@0.135249:0.940361:0.173959:0.940361:0.173959:0.923955:0.135249:0.923955:0.000000:0.000000:0.000000:0.000000:0.000000
':@0.147747:0.939501:0.163081:0.939501:0.163081:0.926603:0.147747:0.926603:0.000000
   :@0.173886:0.940361:0.199494:0.940363:0.199494:0.923930:0.173886:0.923927:0.000000:0.000000:0.000000
u   v   :@0.199420:0.940363:0.250666:0.940363:0.250666:0.923957:0.199420:0.923957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.211919:0.940225:0.218048:0.940225:0.218048:0.926176:0.211919:0.926176:0.000000
5:@0.232111:0.939809:0.247445:0.939809:0.247445:0.926093:0.232111:0.926093:0.000000
0:@0.250592:0.940363:0.259575:0.940363:0.259575:0.923930:0.250592:0.923930:0.000000
Figura 2.11:@0.552021:0.580877:0.630833:0.580877:0.630833:0.564443:0.552021:0.564443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.12:@0.556780:0.921922:0.635593:0.921922:0.635593:0.905488:0.556780:0.905488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.527340:0.876356:0.535071:0.876356:0.535071:0.859950:0.527340:0.859950:0.000000
v:@0.632170:0.882611:0.639901:0.882611:0.639901:0.866205:0.632170:0.866205:0.000000
120°:@0.524631:0.492004:0.550927:0.492004:0.550927:0.478559:0.524631:0.478559:0.000000:0.000000:0.000000:0.000000
x:@0.571044:0.479517:0.578499:0.479517:0.578499:0.463111:0.571044:0.463111:0.000000
    3:@0.578425:0.479517:0.625806:0.479517:0.625806:0.463083:0.578425:0.463083:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.582383:0.478962:0.616915:0.478962:0.616915:0.465246:0.582383:0.465246:0.000000:0.000000:0.000000
0:@0.645685:0.565472:0.654668:0.565472:0.654668:0.549038:0.645685:0.549038:0.000000
a:@0.523682:0.524616:0.532941:0.524616:0.532941:0.508210:0.523682:0.508210:0.000000
a:@0.564402:0.515427:0.575649:0.515427:0.575649:0.501711:0.564402:0.501711:0.000000
y:@0.650023:0.505829:0.657496:0.505829:0.657496:0.489422:0.650023:0.489422:0.000000
   3  3:@0.657367:0.505829:0.706339:0.505829:0.706339:0.489395:0.657367:0.489395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.660846:0.505274:0.676180:0.505274:0.676180:0.491558:0.660846:0.491558:0.000000
La ley de senos para :@0.740294:0.709865:0.876583:0.709865:0.876583:0.694925:0.740294:0.694925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
triángulos oblicuángulos  :@0.740294:0.724994:0.911197:0.724994:0.911197:0.710054:0.740294:0.710054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
establece que::@0.740294:0.740123:0.835677:0.740123:0.835677:0.725183:0.740294:0.725183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.754616:0.815890:0.763452:0.815890:0.763452:0.799484:0.754616:0.799484:0.000000
c:@0.769618:0.782121:0.777276:0.782121:0.777276:0.765715:0.769618:0.765715:0.000000
b:@0.848438:0.781400:0.857697:0.781400:0.857697:0.764994:0.848438:0.764994:0.000000
a:@0.818103:0.821118:0.827362:0.821118:0.827362:0.804712:0.818103:0.804712:0.000000
b:@0.784657:0.800926:0.795904:0.800926:0.795904:0.787210:0.784657:0.787210:0.000000
g:@0.857715:0.804504:0.867950:0.804504:0.867950:0.790788:0.857715:0.790788:0.000000
a:@0.789885:0.772996:0.801131:0.772996:0.801131:0.759280:0.789885:0.759280:0.000000
A:@0.786129:0.753358:0.796014:0.753358:0.796014:0.736952:0.786129:0.736952:0.000000
C:@0.896591:0.815890:0.906494:0.815890:0.906494:0.799484:0.896591:0.799484:0.000000
a:@0.757240:0.833316:0.764816:0.833316:0.764816:0.819893:0.757240:0.819893:0.000000
sen:@0.746035:0.845400:0.766909:0.845400:0.766909:0.831954:0.746035:0.831954:0.000000:0.000000:0.000000
a:@0.766834:0.844946:0.776036:0.844946:0.776036:0.833724:0.766834:0.833724:0.000000
5:@0.781688:0.839264:0.795628:0.839264:0.795628:0.826795:0.781688:0.826795:0.000000
b:@0.812490:0.833316:0.820066:0.833316:0.820066:0.819893:0.812490:0.819893:0.000000
sen:@0.801285:0.845400:0.822159:0.845400:0.822159:0.831954:0.801285:0.831954:0.000000:0.000000:0.000000
b:@0.822084:0.844946:0.831286:0.844946:0.831286:0.833724:0.822084:0.833724:0.000000
5:@0.836939:0.839264:0.850878:0.839264:0.850878:0.826795:0.836939:0.826795:0.000000
c:@0.868397:0.833316:0.874662:0.833316:0.874662:0.819893:0.868397:0.819893:0.000000
sen:@0.856951:0.845400:0.877824:0.845400:0.877824:0.831954:0.856951:0.831954:0.000000:0.000000:0.000000
g:@0.877749:0.844946:0.886123:0.844946:0.886123:0.833724:0.877749:0.833724:0.000000
La ley de cosenos :@0.740294:0.862046:0.860115:0.862046:0.860115:0.847106:0.740294:0.847106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
establece que::@0.740294:0.877175:0.835677:0.877175:0.835677:0.862235:0.740294:0.862235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.740294:0.892304:0.748711:0.892304:0.748711:0.877389:0.740294:0.877389:0.000000
2:@0.748651:0.886791:0.753411:0.886791:0.753411:0.878081:0.748651:0.878081:0.000000
           2:@0.753368:0.892304:0.849355:0.892304:0.849355:0.877364:0.753368:0.877364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.756966:0.891799:0.770905:0.891799:0.770905:0.879331:0.756966:0.879331:0.000000
a:@0.774419:0.892304:0.782836:0.892304:0.782836:0.877389:0.774419:0.877389:0.000000
2:@0.782763:0.886791:0.787523:0.886791:0.787523:0.878081:0.782763:0.878081:0.000000
1:@0.791079:0.891799:0.805019:0.891799:0.805019:0.879331:0.791079:0.879331:0.000000
c:@0.808533:0.892304:0.815494:0.892304:0.815494:0.877389:0.808533:0.877389:0.000000
2:@0.815420:0.886791:0.820181:0.886791:0.820181:0.878081:0.815420:0.878081:0.000000
2:@0.823735:0.891799:0.837675:0.891799:0.837675:0.879331:0.823735:0.879331:0.000000
ac cos:@0.849271:0.892304:0.888300:0.892304:0.888300:0.877389:0.849271:0.877389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.888261:0.892304:0.907204:0.892304:0.907204:0.877364:0.888261:0.877364:0.000000:0.000000:0.000000
b:@0.892629:0.891799:0.902853:0.891799:0.902853:0.879331:0.892629:0.879331:0.000000
a:@0.740300:0.907433:0.748718:0.907433:0.748718:0.892518:0.740300:0.892518:0.000000
2:@0.748651:0.901919:0.753411:0.901919:0.753411:0.893210:0.748651:0.893210:0.000000
           2:@0.753368:0.907432:0.849355:0.907432:0.849355:0.892492:0.753368:0.892492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.756966:0.906928:0.770905:0.906928:0.770905:0.894459:0.756966:0.894459:0.000000
b:@0.774419:0.907432:0.782836:0.907432:0.782836:0.892517:0.774419:0.892517:0.000000
2:@0.782763:0.901919:0.787523:0.901919:0.787523:0.893210:0.782763:0.893210:0.000000
1:@0.791079:0.906928:0.805019:0.906928:0.805019:0.894459:0.791079:0.894459:0.000000
c:@0.808533:0.907432:0.815494:0.907432:0.815494:0.892517:0.808533:0.892517:0.000000
2:@0.815420:0.901919:0.820181:0.901919:0.820181:0.893210:0.815420:0.893210:0.000000
2:@0.823735:0.906928:0.837675:0.906928:0.837675:0.894459:0.823735:0.894459:0.000000
ac cos:@0.849271:0.907432:0.888300:0.907432:0.888300:0.892517:0.849271:0.892517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.888261:0.907432:0.907204:0.907432:0.907204:0.892492:0.888261:0.892492:0.000000:0.000000:0.000000
a:@0.892629:0.906928:0.902853:0.906928:0.902853:0.894459:0.892629:0.894459:0.000000
c:@0.740300:0.922561:0.747262:0.922561:0.747262:0.907646:0.740300:0.907646:0.000000
2:@0.747195:0.917048:0.751956:0.917048:0.751956:0.908339:0.747195:0.908339:0.000000
           2:@0.751912:0.922561:0.849355:0.922561:0.849355:0.907621:0.751912:0.907621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.755510:0.922057:0.769449:0.922057:0.769449:0.909588:0.755510:0.909588:0.000000
a:@0.772963:0.922561:0.781380:0.922561:0.781380:0.907646:0.772963:0.907646:0.000000
2:@0.781307:0.917048:0.786068:0.917048:0.786068:0.908339:0.781307:0.908339:0.000000
1:@0.789623:0.922057:0.803563:0.922057:0.803563:0.909588:0.789623:0.909588:0.000000
b:@0.807077:0.922561:0.815494:0.922561:0.815494:0.907646:0.807077:0.907646:0.000000
2:@0.815420:0.917048:0.820181:0.917048:0.820181:0.908339:0.815420:0.908339:0.000000
2:@0.823735:0.922057:0.837675:0.922057:0.837675:0.909588:0.823735:0.909588:0.000000
ac cos:@0.849271:0.922561:0.888300:0.922561:0.888300:0.907646:0.849271:0.907646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.888261:0.922561:0.906284:0.922561:0.906284:0.907621:0.888261:0.907621:0.000000:0.000000:0.000000
g:@0.892629:0.922057:0.901933:0.922057:0.901933:0.909588:0.892629:0.909588:0.000000
Podemos multiplicar un :@0.740300:0.187786:0.901759:0.187786:0.901759:0.172846:0.740300:0.172846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector por un escalar :@0.740300:0.202915:0.882150:0.202915:0.882150:0.187975:0.740300:0.187975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(número) y el resultado :@0.740300:0.218044:0.897018:0.218044:0.897018:0.203104:0.740300:0.203104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
será otro vector.:@0.740300:0.233173:0.845424:0.233173:0.845424:0.218233:0.740300:0.218233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Practica en tu cuaderno.:@0.740300:0.248302:0.899533:0.248302:0.899533:0.233362:0.740300:0.233362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dado ІІ ІІ 4 y :@0.740300:0.263431:0.838712:0.263431:0.838712:0.248491:0.740300:0.248491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.786938:0.263431:0.795355:0.263431:0.795355:0.248516:0.786938:0.248516:0.000000
5:@0.802199:0.262927:0.816138:0.262927:0.816138:0.250458:0.802199:0.250458:0.000000
a5:@0.838612:0.262927:0.862692:0.262927:0.862692:0.250458:0.838612:0.250458:0.000000:0.000000
5, :@0.862608:0.263431:0.877284:0.263431:0.877284:0.248491:0.862608:0.248491:0.000000:0.000000:0.000000
calcula ІІ:@0.740284:0.278560:0.796509:0.278560:0.796509:0.263620:0.740284:0.263620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.796376:0.278056:0.806600:0.278056:0.806600:0.265587:0.796376:0.265587:0.000000
a:@0.806516:0.278560:0.814933:0.278560:0.814933:0.263645:0.806516:0.263645:0.000000
ІІ:@0.814867:0.278560:0.821861:0.278560:0.821861:0.263620:0.814867:0.263620:0.000000:0.000000
Competencia :@0.740294:0.667387:0.848854:0.667387:0.848854:0.650440:0.740294:0.650440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.684029:0.837769:0.684029:0.837769:0.667082:0.740294:0.667082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.740294:0.145305:0.848854:0.145305:0.848854:0.128358:0.740294:0.128358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.161946:0.837769:0.161946:0.837769:0.145000:0.740294:0.145000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la siguiente :@0.743038:0.436489:0.885062:0.436489:0.885062:0.421549:0.743038:0.421549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simbología matemática::@0.743038:0.451618:0.903569:0.451618:0.903569:0.436678:0.743038:0.436678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• Al producto escalar :@0.743038:0.466747:0.883482:0.466747:0.883482:0.451807:0.743038:0.451807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de dos vectores, lo :@0.743038:0.481876:0.870900:0.481876:0.870900:0.466936:0.743038:0.466936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representamos por el :@0.743038:0.497005:0.888988:0.497005:0.888988:0.482065:0.743038:0.482065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
punto entre los vectores: :@0.743038:0.512134:0.912137:0.512134:0.912137:0.497194:0.743038:0.497194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u   v.:@0.743038:0.527262:0.772640:0.527262:0.772640:0.512348:0.743038:0.512348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.754568:0.527136:0.760140:0.527136:0.760140:0.514365:0.754568:0.514365:0.000000
• Al producto por un :@0.743038:0.542391:0.882562:0.542391:0.882562:0.527452:0.743038:0.527452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
escalar, llamado también :@0.743038:0.557520:0.912361:0.557520:0.912361:0.542581:0.743038:0.542581:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
multiplicación de un :@0.743038:0.572649:0.884406:0.572649:0.884406:0.557709:0.743038:0.557709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector por un escalar, :@0.743038:0.587778:0.888730:0.587778:0.888730:0.572838:0.743038:0.572838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lo representamos sin el :@0.743038:0.602907:0.900787:0.602907:0.900787:0.587967:0.743038:0.587967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
punto: :@0.743038:0.618036:0.790773:0.618036:0.790773:0.603096:0.743038:0.603096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.790746:0.617532:0.800971:0.617532:0.800971:0.605063:0.790746:0.605063:0.000000
u:@0.800971:0.618036:0.809438:0.618036:0.809438:0.603122:0.800971:0.603122:0.000000
.:@0.809455:0.618036:0.812366:0.618036:0.812366:0.603096:0.809455:0.603096:0.000000
Simbología :@0.787249:0.406120:0.881067:0.406120:0.881067:0.389173:0.787249:0.389173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.785417:0.422762:0.879082:0.422762:0.879082:0.405815:0.785417:0.405815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.10:@0.571819:0.385329:0.650144:0.385329:0.650144:0.368895:0.571819:0.368895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.536999:0.351977:0.546313:0.351977:0.546313:0.335571:0.536999:0.335571:0.000000
v:@0.648945:0.349118:0.656676:0.349118:0.656676:0.332712:0.648945:0.332712:0.000000
DBA 5 (Ev. 1) Localiza objetos geométricos en el plano cartesiano.:@0.075755:0.971366:0.419325:0.971366:0.419325:0.959414:0.075755:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000