# The volume of parallelepiped whose sides are given by OA=2i-j ,OB=i+j-k and OC=3i-k is

Solution:  Given   $\vec{OA}=2i-j , \vec{OB}=i+j-k \hspace{0.2cm}\vec{OC}=3i-k$

$volume \hspace{0.2cm}of \hspace{0.2cm}paralelopiped\hspace{0.2cm}=[\vec{a},\vec{b},\vec{c}]\\ \\ \Rightarrow \hspace{1cm}=\begin{vmatrix} 2 &-2 &0 \\ 1& 1 &-1 \\ 3 &0 &-1 \end{vmatrix}=2(-1)+2(-1+3)=2.$

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