Question

SEJAM OS VETORES U=3J+2J+6K , V=-4J-2J+K E W=(2U+3V) - (5K). O PRODUTO MISTO [U,V,W] É:

Answer 1

$\mathrm{u=3i+2j+6k\ \to\ u=(3,2,6)}\\\\ \mathrm{v=-4i-2j+k\ \to\ v=(-4,-2,1)}\\\\ \mathrm{w=(2u+3v)-5k}\\ \mathrm{w=2(3i+2j+6k)+3(-4i-2j+k)-5k}\\ \mathrm{w=6i+4j+12k-12i-6j+3k-5k}\\ \mathrm{w=-6i-2j+10k\ \to\ w=(-6,-2,10)}\\\\ \mathrm{{[u,v,w]=\left|\begin{array}{ccc}u_1&u_2&u_3\\v_1&v_2&v_3\\w_1&w_2&w_3\end{array}\right|= \left|\begin{array}{ccc}3&2&6\\-4&-2&1\\-6&-2&10\end{array}\right|}}$

$\mathrm{{[u,v,w]}=3.(-2).10+2.1.(-6)+6.(-4).(-2)-}\\ \mathrm{-6.(-2).(-6)-3.1.(-2)-2.(-4).10}\\\\ \mathrm{{[u,v,w]}=-60-12+48-72+6+80}\\\\ \mathrm{{[u,v,w]=-144+134}}\ \to\ \mathbf{{[u,v,w]}=-10}$