Al multiplicar un número [b]k[/b] por un vector [img]data:image/png;base64,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[/img] , se obtiene otro vector[b] k·[img]data:image/png;base64,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[/img] [/b]que[br][list=1][*]Conserva la dirección[/*][*] Si k es positivo conserva el sentido y si k es negativo lo cambia[/*][*]Módulo de [b]k·[img]data:image/png;base64,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[/img][/b] es igual a [img]data:image/png;base64,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[/img][/*][/list]
[color=#0b5394][b]OBSERVACIÓN 1:[/b] [/color]Las coordenadas del vector [img]data:image/png;base64,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[/img] se obtienen multiplicando por k las coordenadas de [img]data:image/png;base64,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[/img].[br][br]Ejemplo: [img]data:image/png;base64,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[/img]= (5, -2) el vector [b]3[/b][b][img]data:image/png;base64,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[/img][/b]=(3·5 , 3·(-2))=(15 , -6)[br][br][b][br][color=#b45f06]OBSERVACIÓN 2:[/color] [/b]Dos vectores son paralelos, si tienen la misma dirección. Todos los vectores que se obtienen multiplicando por un número otro vector, son paralelos. [br]Por tanto, dos vectores son paralelos si tienen sus coordenadas proporcionales.[br][br]Ejemplo: ¿Son paralelos los vectores [img]data:image/png;base64,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[/img](-2,6) y [img]data:image/png;base64,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[/img]( 3,-9) ?[br]Estudiamos si sus coordenadas son proporcionales. Comprobamos que podemos escribir con sus coordenadas la proporción [math]\frac{-2}{3}=\frac{6}{-9}[/math] , entonces los vectores son paralelos.
[b]Página 162. Ejercicio 2[/b]