Question

Dados os vetores U = (3, -1, 2) e V = (-2, 2, 1), calcule a área do paralelogramo determinado por U e V.

Answer 1

 U = (3, -1, 2)
 V = (-2, 2, 1)

$\left[\begin{array}{ccc}i&j&k\\3&-1&2\\-2&2&1\end{array}\right] \left\begin{array}{cc}i&j\\3&-1\\-2&2\end{array}\right] \\\\\ i=(-1-4)=-5\\\\j=(-4-3)=-7\\\\k=(6-2)=4\\\\\\\\\ (-5 ;-7;4)$

calculando o modulo disso
$\sqrt{(-5)^2+(;-7)^2+(4)^2} \\\\ \sqrt{25+49+16} \\\\ \sqrt{90}$

a área desse paralelogramo vale √90