Answer to Question #120180 in Mechanical Engineering for Pkm

Question

Calculate the volume of a parallelopiped whose vertices are given by (0,0,0),
(2,1,3),(3,2,4) and (4,2,1).

Answer 1

(https://en.wikipedia.org/wiki/Triple_product#/media/File:Parallelepiped_volume.svg)

So,

$a=(2,1,3); b=(3,2,4); c=(4,2,1).$

$V=a\cdot(b\times c)=\begin{vmatrix} 3 & 2&4 \\ 2 & 1 &3\\ 4&2&1 \end{vmatrix}=5$