72:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000 Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000 Actividad resuelta:@0.115209:0.519972:0.272331:0.519972:0.272331:0.501535:0.115209:0.501535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Hallamos:@0.115209:0.539818:0.186469:0.539818:0.186469:0.523194:0.115209:0.523194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la ecuación vectorial y las ecuaciones paramétricas de la recta, que pasa por los puntos:@0.186469:0.539818:0.825698:0.539818:0.825698:0.523429:0.186469:0.523429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = 3, 2, 1 y = –1, 1, 0:@0.115209:0.558337:0.310850:0.558332:0.310850:0.541943:0.115209:0.541948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.119245:0.555073:0.122562:0.555073:0.122562:0.538712:0.119245:0.538712:0.000000 p:@0.119245:0.558849:0.128514:0.558849:0.128514:0.542488:0.119245:0.542488:0.000000 (:@0.147650:0.559010:0.153786:0.559010:0.153786:0.543437:0.147650:0.543437:0.000000 ):@0.195248:0.559010:0.201385:0.559010:0.201385:0.543437:0.195248:0.543437:0.000000 q:@0.225636:0.557585:0.234905:0.557585:0.234905:0.541224:0.225636:0.541224:0.000000 (:@0.254038:0.559010:0.260174:0.559010:0.260174:0.543437:0.254038:0.543437:0.000000 ):@0.310850:0.559010:0.316986:0.559010:0.316986:0.543437:0.310850:0.543437:0.000000 Primero :@0.115204:0.582051:0.176586:0.582051:0.176586:0.565662:0.115204:0.565662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 calculamos:@0.176586:0.582051:0.262496:0.582051:0.262496:0.565427:0.176586:0.565427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la dirección de la recta por medio de::@0.262496:0.582051:0.538245:0.582051:0.538245:0.565662:0.262496:0.565662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = – ; = 4, 1, 1:@0.115204:0.599311:0.274951:0.599313:0.274951:0.582924:0.115204:0.582922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.119239:0.599823:0.128508:0.599823:0.128508:0.583462:0.119239:0.583462:0.000000 p q b:@0.147650:0.599824:0.208218:0.599824:0.208218:0.583463:0.147650:0.583463:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.227353:0.599990:0.233489:0.599990:0.233489:0.584417:0.227353:0.584417:0.000000 ):@0.274951:0.599990:0.281088:0.599990:0.281088:0.584417:0.274951:0.584417:0.000000 Encontramos:@0.115202:0.624207:0.216609:0.624207:0.216609:0.607583:0.115202:0.607583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que la ecuación vectorial es: = + ; = 3, 2, 1 + 4, 1, 1 , :@0.216609:0.624207:0.690779:0.624206:0.690779:0.607817:0.216609:0.607818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.430514:0.624207:0.437977:0.624207:0.437977:0.607846:0.430514:0.607846:0.000000 p:@0.457815:0.624718:0.467084:0.624718:0.467084:0.608356:0.457815:0.608356:0.000000 tb x:@0.486221:0.624206:0.523728:0.624206:0.523728:0.607845:0.486221:0.607845:0.000000:0.000000:0.000000:0.000000 (:@0.543561:0.624884:0.549697:0.624884:0.549697:0.609311:0.543561:0.609311:0.000000 ):@0.591159:0.624884:0.597296:0.624884:0.597296:0.609311:0.591159:0.609311:0.000000 t:@0.616350:0.624206:0.621731:0.624206:0.621731:0.607845:0.616350:0.607845:0.000000 (:@0.621731:0.624884:0.627867:0.624884:0.627867:0.609311:0.621731:0.609311:0.000000 ) ∀ ∈:@0.669329:0.624884:0.725755:0.624884:0.725755:0.609311:0.669329:0.609311:0.000000:0.000000:0.000000:0.000000:0.000000 t :@0.703918:0.624206:0.729072:0.624206:0.729072:0.607845:0.703918:0.607845:0.000000:0.000000:0.000000:0.000000 R:@0.729072:0.623348:0.742377:0.623348:0.742377:0.610486:0.729072:0.610486:0.000000 Determinamos :@0.115210:0.663470:0.233590:0.663470:0.233590:0.646846:0.115210:0.646846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas: = 2 + , :@0.233590:0.663470:0.538972:0.663401:0.538972:0.647012:0.233590:0.647081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.459660:0.646805:0.467123:0.646805:0.467123:0.630443:0.459660:0.630443:0.000000 = 3 + 4:@0.467123:0.646805:0.523217:0.646805:0.523217:0.630416:0.467123:0.630416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t:@0.523217:0.646805:0.528598:0.646805:0.528598:0.630443:0.523217:0.630443:0.000000 y:@0.459660:0.663401:0.467141:0.663401:0.467141:0.647040:0.459660:0.647040:0.000000 t:@0.514242:0.663401:0.519623:0.663401:0.519623:0.647040:0.514242:0.647040:0.000000 ∀ ∈ :@0.538972:0.664079:0.579274:0.664079:0.579274:0.648506:0.538972:0.648506:0.000000:0.000000:0.000000:0.000000 t:@0.552111:0.663401:0.557492:0.663401:0.557492:0.647040:0.552111:0.647040:0.000000 :@0.557492:0.663401:0.561528:0.663401:0.561528:0.647012:0.557492:0.647012:0.000000 R:@0.579274:0.662544:0.592578:0.662544:0.592578:0.649681:0.579274:0.649681:0.000000 z:@0.459660:0.679997:0.466902:0.679997:0.466902:0.663636:0.459660:0.663636:0.000000 = 1 + :@0.466902:0.679997:0.514003:0.679997:0.514003:0.663608:0.466902:0.663608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t:@0.514003:0.679997:0.519384:0.679997:0.519384:0.663636:0.514003:0.663636:0.000000 2. :@0.506905:0.784594:0.525646:0.784594:0.525646:0.767458:0.506905:0.767458:0.000000:0.000000:0.000000 Sea la ecuación vectorial = (1, 4, 2) + (1, 1, 1), :@0.540148:0.784594:0.882959:0.784594:0.882959:0.768205:0.540148:0.768205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.723317:0.784594:0.730780:0.784594:0.730780:0.768232:0.723317:0.768232:0.000000 t:@0.819550:0.784594:0.824931:0.784594:0.824931:0.768232:0.819550:0.768232:0.000000 determina :@0.540150:0.801190:0.623793:0.801190:0.623793:0.784566:0.540150:0.784566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas.:@0.623793:0.801190:0.831819:0.801190:0.831819:0.784801:0.623793:0.784801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Taller:@0.174199:0.742834:0.235094:0.742834:0.235094:0.708886:0.174199:0.708886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 I.M.5.7.1. Opera analítica, geométrica y gráficamente, con vectores, rectas y planos en el espacio; expresa la ecuación de la recta de :@0.255220:0.720298:0.875876:0.720298:0.875876:0.709868:0.255220:0.709868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 forma paramétrica y vectorial; halla mediante tres puntos dicha ecuación o a partir de la intersección de dos planos, y determina la :@0.255220:0.730859:0.875992:0.730859:0.875992:0.720430:0.255220:0.720430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ortogonalidad de los mismos, para efectuar aplicaciones geométricas. (I.2.):@0.255220:0.741420:0.601468:0.741420:0.601468:0.730991:0.255220:0.730991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ecuación vectorial y paramétrica de una recta en el espacio:@0.115891:0.143735:0.884926:0.143735:0.884926:0.102998:0.115891:0.102998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M.5.2.20. Escribir y reconocer la ecuación vectorial y paramétrica de una recta a partir de un punto de la recta y un vector dirección, o a partir de dos puntos de la :@0.125388:0.069719:0.877827:0.069719:0.877827:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 recta, y graficarlas en 3.:@0.125388:0.080280:0.238855:0.080280:0.238855:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.225192:0.079734:0.233659:0.079734:0.233659:0.071549:0.225192:0.071549:0.000000 1:@0.059451:0.122645:0.071060:0.122645:0.071060:0.065614:0.059451:0.065614:0.000000 Ecuación vectorial de la recta en el plano :@0.160345:0.180504:0.460159:0.180504:0.460159:0.165140:0.160345:0.165140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que pasa por dos puntos:@0.217772:0.195592:0.395780:0.195592:0.395780:0.180228:0.217772:0.180228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ecuación vectorial de la recta :@0.584164:0.180504:0.800752:0.180504:0.800752:0.165140:0.584164:0.165140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que pasa por dos puntos en el espacio:@0.551597:0.195592:0.826383:0.195592:0.826383:0.180228:0.551597:0.180228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La ecuación = + ; :@0.122367:0.222259:0.282513:0.222257:0.282513:0.207358:0.122367:0.207360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.205777:0.222574:0.212562:0.222574:0.212562:0.207700:0.205777:0.207700:0.000000 a:@0.231346:0.221817:0.239773:0.221817:0.239773:0.206943:0.231346:0.206943:0.000000 tb:@0.258020:0.222257:0.271338:0.222295:0.271338:0.207421:0.258020:0.207383:0.000000:0.000000 ∀ ∈:@0.282513:0.222873:0.314309:0.222873:0.314309:0.208716:0.282513:0.208716:0.000000:0.000000:0.000000 t :@0.294458:0.222257:0.317325:0.222257:0.317325:0.207383:0.294458:0.207383:0.000000:0.000000:0.000000:0.000000 R :@0.317325:0.221477:0.333441:0.221477:0.333441:0.209784:0.317325:0.209784:0.000000:0.000000 se conoce como :@0.333441:0.222257:0.447709:0.222257:0.447709:0.207358:0.333441:0.207358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuación vectorial de la recta . El vector se llama :@0.122377:0.238514:0.467389:0.238514:0.467389:0.223615:0.122377:0.223615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.320337:0.238514:0.328478:0.238514:0.328478:0.223640:0.320337:0.223640:0.000000 b:@0.395877:0.238828:0.404303:0.238828:0.404303:0.223954:0.395877:0.223954:0.000000 vector director de la recta . :@0.122374:0.253601:0.311406:0.253601:0.311406:0.238702:0.122374:0.238702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.296681:0.253601:0.304822:0.253601:0.304822:0.238728:0.296681:0.238728:0.000000 = – = 1 2 – 1 2:@0.122374:0.274171:0.306416:0.274170:0.306416:0.259271:0.122374:0.259272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.126043:0.274485:0.134469:0.274485:0.134469:0.259611:0.126043:0.259611:0.000000 p q:@0.152620:0.273730:0.186112:0.274207:0.186112:0.259333:0.152620:0.258856:0.000000:0.000000:0.000000 (:@0.204357:0.275162:0.210493:0.275162:0.210493:0.259589:0.204357:0.259589:0.000000 a , a:@0.210493:0.274484:0.239202:0.274484:0.239202:0.258123:0.210493:0.258123:0.000000:0.000000:0.000000:0.000000:0.000000 ) (:@0.243993:0.275162:0.272917:0.275162:0.272917:0.259589:0.243993:0.259589:0.000000:0.000000:0.000000:0.000000 b , b:@0.272917:0.274484:0.301626:0.274484:0.301626:0.258123:0.272917:0.258123:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.306416:0.275162:0.312552:0.275162:0.312552:0.259589:0.306416:0.259589:0.000000 b:@0.122374:0.294645:0.130800:0.294645:0.130800:0.279771:0.122374:0.279771:0.000000 = 1 – 1 2 – 2:@0.131629:0.294330:0.249089:0.294330:0.249089:0.279431:0.131629:0.279431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( :@0.148951:0.295322:0.172482:0.295322:0.172482:0.279749:0.148951:0.279749:0.000000:0.000000:0.000000 a:@0.155088:0.294645:0.164357:0.294645:0.164357:0.278283:0.155088:0.278283:0.000000 b , a:@0.184527:0.294645:0.213587:0.294645:0.213587:0.278283:0.184527:0.278283:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.218377:0.295322:0.222984:0.295322:0.222984:0.279749:0.218377:0.279749:0.000000 b:@0.235029:0.294645:0.244298:0.294645:0.244298:0.278283:0.235029:0.278283:0.000000 ):@0.249089:0.295322:0.255225:0.295322:0.255225:0.279749:0.249089:0.279749:0.000000 Las ecuaciones paramétricas de la recta son::@0.122374:0.312982:0.427966:0.312982:0.427966:0.298083:0.122374:0.298083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.389100:0.312982:0.397242:0.312982:0.397242:0.298109:0.389100:0.298109:0.000000 x:@0.132140:0.331326:0.138925:0.331326:0.138925:0.316453:0.132140:0.316453:0.000000 = + :@0.138925:0.331326:0.181996:0.331326:0.181996:0.316427:0.138925:0.316427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.156247:0.331326:0.164674:0.331326:0.164674:0.316453:0.156247:0.316453:0.000000 tc,:@0.181996:0.331326:0.196669:0.331326:0.196669:0.316453:0.181996:0.316453:0.000000:0.000000:0.000000 y:@0.132140:0.346414:0.138942:0.346414:0.138942:0.331540:0.132140:0.331540:0.000000 = + :@0.138942:0.346414:0.182012:0.346414:0.182012:0.331515:0.138942:0.331515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.156264:0.346414:0.164690:0.346414:0.164690:0.331540:0.156264:0.331540:0.000000 td.:@0.182012:0.346414:0.198011:0.346414:0.198011:0.331540:0.182012:0.331540:0.000000:0.000000:0.000000 Siendo:@0.122374:0.375293:0.168778:0.375293:0.168778:0.360394:0.122374:0.360394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.168776:0.375607:0.201217:0.375607:0.201217:0.359218:0.168776:0.359218:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.172812:0.372343:0.176129:0.372343:0.176129:0.355982:0.172812:0.355982:0.000000 u:@0.172812:0.376119:0.182136:0.376119:0.182136:0.359758:0.172812:0.359758:0.000000 (:@0.201217:0.376285:0.207354:0.376285:0.207354:0.360712:0.201217:0.360712:0.000000 a, b:@0.207354:0.375607:0.232544:0.375607:0.232544:0.359246:0.207354:0.359246:0.000000:0.000000:0.000000:0.000000 ):@0.232544:0.376285:0.238681:0.376285:0.238681:0.360712:0.232544:0.360712:0.000000 , :@0.238681:0.375293:0.252602:0.375293:0.252602:0.360394:0.238681:0.360394:0.000000:0.000000:0.000000:0.000000 :@0.252602:0.372345:0.255919:0.372345:0.255919:0.355983:0.252602:0.355983:0.000000 v:@0.252602:0.376120:0.260341:0.376120:0.260341:0.359759:0.252602:0.359759:0.000000 = :@0.261951:0.375607:0.281006:0.375607:0.281006:0.359218:0.261951:0.359218:0.000000:0.000000:0.000000 (:@0.281006:0.376285:0.287142:0.376285:0.287142:0.360712:0.281006:0.360712:0.000000 c, d .:@0.287142:0.375607:0.320017:0.375607:0.320017:0.359246:0.287142:0.359246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.310545:0.376285:0.316681:0.376285:0.316681:0.360712:0.310545:0.360712:0.000000 Dados los puntos:@0.504595:0.217196:0.620721:0.217196:0.620721:0.202297:0.504595:0.202297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.504595:0.237388:0.513021:0.237388:0.513021:0.222515:0.504595:0.222515:0.000000 = 1 2 3 = 1 2 3 :@0.513944:0.237357:0.705954:0.237357:0.705954:0.222458:0.513944:0.222458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.531266:0.238349:0.537403:0.238349:0.537403:0.222776:0.531266:0.222776:0.000000 a , a , a ,:@0.537403:0.237671:0.600970:0.237671:0.600970:0.221310:0.537403:0.221310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ) :@0.591498:0.238349:0.605577:0.238349:0.605577:0.222776:0.591498:0.222776:0.000000:0.000000:0.000000 q:@0.609245:0.237395:0.617672:0.237395:0.617672:0.222521:0.609245:0.222521:0.000000 (:@0.635917:0.238349:0.642053:0.238349:0.642053:0.222776:0.635917:0.222776:0.000000 b , b , b:@0.642053:0.237671:0.691474:0.237671:0.691474:0.221310:0.642053:0.221310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.696147:0.238349:0.702283:0.238349:0.702283:0.222776:0.696147:0.222776:0.000000 ∈:@0.705954:0.237973:0.717898:0.237973:0.717898:0.223816:0.705954:0.223816:0.000000 :@0.717898:0.237357:0.720913:0.237357:0.720913:0.222483:0.717898:0.222483:0.000000 R:@0.720913:0.236578:0.733009:0.236578:0.733009:0.224885:0.720913:0.224885:0.000000 3 con ≠ , :@0.732841:0.237357:0.821094:0.237357:0.821094:0.222458:0.732841:0.222458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.777553:0.237395:0.785980:0.237395:0.785980:0.222521:0.777553:0.222521:0.000000 :@0.800553:0.238349:0.805160:0.238349:0.805160:0.222776:0.800553:0.222776:0.000000 q:@0.805160:0.237391:0.813586:0.237391:0.813586:0.222517:0.805160:0.222517:0.000000 se deduce que::@0.504591:0.256003:0.606161:0.256003:0.606161:0.241104:0.504591:0.241104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • El vector director de la recta es::@0.504591:0.275818:0.758990:0.275829:0.758990:0.260930:0.504591:0.260919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.644893:0.276132:0.653319:0.276132:0.653319:0.261258:0.644893:0.261258:0.000000 R :@0.730544:0.275829:0.741701:0.275829:0.741701:0.260955:0.730544:0.260955:0.000000:0.000000 = 1 – 1 2 – 2 3 – 3:@0.504590:0.295984:0.707828:0.295989:0.707828:0.281090:0.504590:0.281085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.530271:0.296298:0.538698:0.296298:0.538698:0.281424:0.530271:0.281424:0.000000 ( :@0.556854:0.296981:0.580384:0.296981:0.580384:0.281408:0.556854:0.281408:0.000000:0.000000:0.000000 a:@0.562990:0.296303:0.572259:0.296303:0.572259:0.279942:0.562990:0.279942:0.000000 b , a:@0.592428:0.296303:0.621136:0.296303:0.621136:0.279942:0.592428:0.279942:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.625927:0.296981:0.630534:0.296981:0.630534:0.281408:0.625927:0.281408:0.000000 b , a:@0.642579:0.296303:0.672561:0.296303:0.672561:0.279942:0.642579:0.279942:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.677235:0.296981:0.681842:0.296981:0.681842:0.281408:0.677235:0.281408:0.000000 b:@0.693887:0.296303:0.703156:0.296303:0.703156:0.279942:0.693887:0.279942:0.000000 ):@0.707828:0.296981:0.713965:0.296981:0.713965:0.281408:0.707828:0.281408:0.000000 • La ecuación vectorial de la recta es::@0.504595:0.314641:0.774171:0.314641:0.774171:0.299742:0.504595:0.299742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.745072:0.314641:0.753214:0.314641:0.753214:0.299767:0.745072:0.299767:0.000000 = + :@0.504595:0.335713:0.582512:0.335718:0.582512:0.320819:0.504595:0.320814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.530276:0.334770:0.537061:0.334770:0.537061:0.319896:0.530276:0.319896:0.000000 p:@0.555839:0.335278:0.564265:0.335278:0.564265:0.320404:0.555839:0.320404:0.000000 tb:@0.582512:0.335718:0.595830:0.335857:0.595830:0.320983:0.582512:0.320844:0.000000:0.000000 = 1 2 3:@0.504595:0.360360:0.611775:0.360360:0.611775:0.345461:0.504595:0.345461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.530276:0.359417:0.537061:0.359417:0.537061:0.344543:0.530276:0.344543:0.000000 (:@0.555839:0.360976:0.561417:0.360976:0.561417:0.346819:0.555839:0.346819:0.000000 a , a , a + t a:@0.561417:0.360360:0.652265:0.360360:0.652265:0.345486:0.561417:0.345486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.611775:0.360976:0.617353:0.360976:0.617353:0.346819:0.611775:0.346819:0.000000 ( :@0.638260:0.360976:0.659972:0.360976:0.659972:0.346819:0.638260:0.346819:0.000000:0.000000:0.000000 1 – 1 2 – 2 3 – 3 , :@0.652265:0.360360:0.793974:0.360360:0.793974:0.345461:0.652265:0.345461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b , a:@0.672017:0.360360:0.699088:0.360360:0.699088:0.345486:0.672017:0.345486:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.703880:0.360976:0.708068:0.360976:0.708068:0.346819:0.703880:0.346819:0.000000 b , a:@0.720113:0.360360:0.747804:0.360360:0.747804:0.345486:0.720113:0.345486:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.752478:0.360976:0.756666:0.360976:0.756666:0.346819:0.752478:0.346819:0.000000 b:@0.768711:0.360360:0.777138:0.360360:0.777138:0.345486:0.768711:0.345486:0.000000 ) ∀ ∈:@0.781812:0.360976:0.834146:0.360976:0.834146:0.346819:0.781812:0.346819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t :@0.814295:0.360360:0.837162:0.360360:0.837162:0.345486:0.814295:0.345486:0.000000:0.000000:0.000000:0.000000 R:@0.837162:0.359581:0.849257:0.359581:0.849257:0.347888:0.837162:0.347888:0.000000 Ecuación vectorial de la recta en el espacio cuando Ecuación paramétrica de la recta en el espacio:@0.122370:0.398205:0.835669:0.398207:0.835669:0.382843:0.122370:0.382841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se conoce un punto y el vector director:@0.122370:0.413292:0.401980:0.413292:0.401980:0.397928:0.122370:0.397928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea el punto 0 = ( 0, 0, 0) y el vector director :@0.122370:0.431938:0.429673:0.431938:0.429673:0.417039:0.122370:0.417039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.209749:0.431938:0.217723:0.431938:0.217723:0.417064:0.209749:0.417064:0.000000 x y z:@0.244678:0.431938:0.288402:0.431938:0.288402:0.417064:0.244678:0.417064:0.000000:0.000000:0.000000:0.000000:0.000000 = (v1, v2, v3), la ecuación vectorial de la recta que pasa :@0.122370:0.448535:0.494341:0.448543:0.494341:0.433644:0.122370:0.433636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.126043:0.445595:0.129359:0.445595:0.129359:0.429234:0.126043:0.429234:0.000000 v:@0.126043:0.449371:0.133782:0.449371:0.133782:0.433009:0.126043:0.433009:0.000000 :@0.135392:0.448858:0.139428:0.448858:0.139428:0.432469:0.135392:0.432469:0.000000 por 0 y es paralela al vector director es: :@0.122374:0.464951:0.405019:0.464945:0.405019:0.450046:0.122374:0.450052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.149144:0.464951:0.157118:0.464951:0.157118:0.450077:0.149144:0.450077:0.000000 :@0.367373:0.461997:0.370690:0.461997:0.370690:0.445635:0.367373:0.445635:0.000000 v:@0.367373:0.465772:0.375112:0.465772:0.375112:0.449411:0.367373:0.449411:0.000000 (:@0.122372:0.480032:0.126811:0.480032:0.126811:0.465133:0.122372:0.465133:0.000000 x, y, z:@0.126811:0.480032:0.158473:0.480032:0.158473:0.465159:0.126811:0.465159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ) = ( 0, 0, 0) + ( 1, 2, 3):@0.158473:0.480032:0.316382:0.480032:0.316382:0.465133:0.158473:0.465133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.184674:0.480032:0.228398:0.480032:0.228398:0.465159:0.184674:0.465159:0.000000:0.000000:0.000000:0.000000:0.000000 t v v v:@0.255353:0.480032:0.307268:0.480032:0.307268:0.465159:0.255353:0.465159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 De la ecuación vectorial de la recta en el espacio se :@0.504595:0.416853:0.849054:0.416853:0.849054:0.401954:0.504595:0.401954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 desprenden las ecuaciones paramétricas así::@0.504595:0.431941:0.799398:0.431941:0.799398:0.417042:0.504595:0.417042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.514361:0.449618:0.521146:0.449618:0.521146:0.434745:0.514361:0.434745:0.000000 = 0 + 1:@0.521146:0.449618:0.583415:0.449618:0.583415:0.434719:0.521146:0.434719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.538468:0.449618:0.545253:0.449618:0.545253:0.434745:0.538468:0.434745:0.000000 tv:@0.567768:0.449618:0.579897:0.449618:0.579897:0.434745:0.567768:0.434745:0.000000:0.000000 y:@0.514361:0.464706:0.521163:0.464706:0.521163:0.449832:0.514361:0.449832:0.000000 = 0 + 2:@0.521163:0.464706:0.584721:0.464706:0.584721:0.449807:0.521163:0.449807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.538485:0.464706:0.545286:0.464706:0.545286:0.449832:0.538485:0.449832:0.000000 tv:@0.567802:0.464706:0.579930:0.464706:0.579930:0.449832:0.567802:0.449832:0.000000:0.000000 z:@0.514361:0.479794:0.520945:0.479794:0.520945:0.464920:0.514361:0.464920:0.000000 = 0 + 3:@0.520945:0.479794:0.584169:0.479794:0.584169:0.464895:0.520945:0.464895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.538267:0.479794:0.544851:0.479794:0.544851:0.464920:0.538267:0.464920:0.000000 tv:@0.567366:0.479794:0.579495:0.479794:0.579495:0.464920:0.567366:0.464920:0.000000:0.000000 1. :@0.113874:0.784594:0.132614:0.784594:0.132614:0.767458:0.113874:0.767458:0.000000:0.000000:0.000000 Sea la ecuación vectorial = (3, 7, –1), :@0.147117:0.784594:0.438894:0.784594:0.438894:0.768205:0.147117:0.768205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.334858:0.784594:0.342321:0.784594:0.342321:0.768232:0.334858:0.768232:0.000000 t:@0.363985:0.784594:0.369366:0.784594:0.369366:0.768232:0.363985:0.768232:0.000000 obtén :@0.439815:0.784594:0.489772:0.784594:0.489772:0.767970:0.439815:0.767970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ecuaciones paramétricas.:@0.147110:0.801190:0.355136:0.801190:0.355136:0.784801:0.147110:0.784801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000