# Can we able to find the volume of parallelopipe or a cuboid or the volume something using determinant method ?

Dec 12, 2017

See below.

#### Explanation:

Given

$a = \left({a}_{1} , {a}_{2} , {a}_{3}\right)$
$b = \left({b}_{1} , {b}_{2} , {b}_{3}\right)$
$c = \left({c}_{1} , {c}_{2} , {c}_{3}\right)$

we have

$\left(a \times b\right) \cdot c = \det \left(\begin{matrix}a \\ b \\ c\end{matrix}\right)$

and

$V = \left\mid \left(a \times b\right) \cdot c \right\mid$

where $V$ is the volume of the prism having as base area $\left\mid a \times b \right\mid$ and main edge $c$.