Dados os pontos A = (1,3), B = (-2, 3), C = (2, -4) e D = (5, -1), determine as coordenadas do vetor V, tal que V = 2.VAB+3.VAC - 5VAD

Para encontrar as coordenadas de V, devemos realizar os cálculos abaixo:

\(\begin{align} & A=(1,3) \\ & B=(-2,3) \\ & C=(2,-4) \\ & D=(5,-1) \\ & \\ & V=2VAB+3VAC-5VAD \\ & (x,y)=(2x,2y)(-2-1,3-3)+(3x,3y)(1,-7)+(5x,5y)(4,-4) \\ & (x,y)=(2x,2y)(-3,0)+(3x,3y)(1,-7)+(5x,5y)(4,-4) \\ & (x,y)=(-6x,0)+(3x,-21y)+(20x,-20y) \\ & (x,y)=(-19x,-41y) \\ & V=(-19,-41) \\ \end{align} \)

Portanto, as coordenadas de V serão \(\boxed{{\text{v}}\left( { - 19, - 41} \right)}\) .