Question

– Dados os pontos A(2, -1, 2), B(1, 2, -1) e C(3, 2, 1), determinar o vetor CB x (BC − 2CA)

Answer 1

$u=CB=B-C=(1,2,-1)-(3,2,1)=(-2,0,-2) \\ \\ v=BC=C-B=(3,2,1)-(1,2,-1)=(2,0,2) \\ \\ w=CA=A-C=(2,-1,2)-(3,2,1)=(-1,-3,1) \\ \\ \\ u \times (v-2w) \\ \\ u \times [(2,0,2)-2 \cdot (-1,-3,1)] \\ \\ u \times [(2,0,2)-(-2,-6,2)] \\ \\ u \times (4,6,0) \\ \\ u \times x$

$\left[\begin{array}{ccc}i&j&k\\-2&0&-2\\4&6&0\end{array}\right] = 12i-8j -12k \\ \\ \\ \boxed{\boxed{y=(12,-8,-12)}}$