Answer:
Let \[\vec{a}=-\,3\hat{i}+7\hat{j}+5k,\] \[\vec{b}=-\,5\hat{i}+7\hat{j}-3k\] and \[\vec{c}=7\hat{i}-5\hat{j}-3k.\] We know that, the volume of a parallelepiped whose three adjacent edges are \[\vec{a},\,\,\vec{b},\,\,\vec{c}\] is equal to \[\left| [\vec{a},\,\,\vec{b},\,\,\vec{c}] \right|.\] Here, \[\Rightarrow \] \[[\begin{matrix} {\vec{a}} & {\vec{b}} & {\vec{c}} \\ \end{matrix}]=-\,3(-2\,1-15)-7(15+21)\] \[+5(25-49)\] \[\Rightarrow \] \[[\begin{matrix} {\vec{a}} & {\vec{b}} & {\vec{c}} \\ \end{matrix}]=108-252-120=-\,264\] Hence, volume of the parallelepiped \[|[\begin{matrix} {\vec{a}} & {\vec{b}} & {\vec{c}} \\ \end{matrix}]|\,\,=\,\,|-\,264|\,\,=264\] cu units.
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