Answer
18 cubic units
Work Step by Step
To find the volume of the parallelepiped with one vertex at
the origin;
given the vertices as ;
$\textbf{v1}=\begin{bmatrix}1\\3\\0\end{bmatrix}$
$\textbf{v2}=\begin{bmatrix}-2\\0\\2\end{bmatrix}$
$\textbf{v3}=\begin{bmatrix}-1\\3\\-1\end{bmatrix}$
the adjacent vectors form a Matrix $\textbf{A}$
$\textbf{A}=\begin{bmatrix}1&-2&-1\\3&0&3\\0&2&-1\end{bmatrix}$
volume of the parallelepiped is found as;
$volume= |det A|=|1\begin{vmatrix}0&3\\2&-1\end{vmatrix}-3\begin{vmatrix}-2&-1\\2&-1\end{vmatrix}+0\begin{vmatrix}-2&-1\\0&3\end{vmatrix}|$
$volume=|1(0-6)-3(2+2)|=|-18|=18$ cubic units