Question

Dados os vetores u=(5,x,-2) , v=(x,3,2) e os pontos A(-1,5,-2) e B(3,2,4), determinar o valor de x tal que u.(v+BA)=10.

Answer 1

vamos determinar o vetor BA

$\\ BA = A - B \\ \\ BA = (-1,5,-2) - (3, 2, 4) \\ \\ BA = (-1-3, 5-2, -2-4) \\ \\ BA = (-4, 3, -6)$

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∵

u.(v + BA) = 10 

$\\ (5, x , -2).[(x,3,2)+(-4,3,-6)] = 10 \\ \\ (5, x , -2).(x-4,3+3,2-6)=10 \\ \\ (5, x , -2).(x-4, 6, -4) = 10 \\ \\ 5(x-4)+x(6)-2(-4)=10 \\ \\ 5x-20+6x+8=10 \\ \\ 11x-12=10 \\ \\ 11x=10+12 \\ \\ 11x=22 \\ \\ x = \frac{22}{11}$

x = 2