Question

Calcular o valor de m para que o volume do paralelepípedo determinado por  u ( 2,m,-3), v ( 2,-4,,5) e w ( -1,-2,7) seja 10 unidades de volume.

Answer 1

$\boxed{\boxed{Volume = ||(\vec U_X\vec V)*\vec W||}}$

.
$(\vec U_X\vec V)*\vec W = \left[\begin{array}{ccc}2&m&-3\\2&-4&5\\-1&-2&7\end{array}\right] =-19m-12=-(19m+12)$

então
$Volume = ||-(19m+12)||$

ele quer que o volume seja 10
$\boxed{10 = ||-(19m+12)||}$

logo
$10=-(19m+12)\\ -10 = 19m+12\\-10-12=19m\\\\ \frac{-22}{19} =m$

ou 
$-10=-(19m+12)\\10=19m+12\\\\ \frac{10-12}{19}=m\\\\ \frac{-2}{19} =m$