Question

Calcular o produto misto dos vetores u=3i-2j+k , v=-i-j-k e w=4i+3k.

possíveis respostas:

-17
-3
15
-10
7

Answer 1

$Sabemos\ que:\\\\ u=3i-2j+k\ \| \ (u_1,u_2,u_3)=(3,-2,1) \\ v=-i-j-k\ \| \ (v_1,v_2,v_3)=(-1,-1,-1) \\ w=4i+3k\ \| \ (w_1,w_2,w_3)=(4,0,3) \\\\ Calculando\ {[u,v,w]}:\\\\ {[u,v,w]}=\left[\begin{array}{ccc}u_1&u_2&u_3\\v_1&v_2&v_3\\w_1&w_2&w_3\end{array}\right]\\\\\\ {[u,v,w]}=\left[\begin{array}{ccc}3&-2&1\\-1&-1&-1\\4&0&3\end{array}\right]\\\\\\ {[u,v,w]}=3.(-1).3+(-2).(-1).4-1.(-1).4-(-2).(-1).3\\\\ {[u,v,w]}=-9+8+4-6\\\\ {[u,v,w]}=12-15\\\\ {[u,v,w]}=-3$