The volume of parallelopiped whose co-terminous are given by $-3\hat{i} + 7 \hat{j} + 5\hat{k}, - 5\hat{i} + 7\hat{j} - 3\hat{k} $ and $7\hat{i}-5\hat{j} - 3\hat{k}$ is :

264 cubic unit

The correct answer is Option (3) → 264 cubic unit

Volume = Δ = $\begin{vmatrix}-3&7&5\\-5&7&-3\\7&-5&-3\end{vmatrix}$

$C_1→C_1+C_2+C_3$

$\begin{vmatrix}9&7&5\\-1&7&-3\\-1&-5&-3\end{vmatrix}$

$R_2→R_2-R_3$

$\begin{vmatrix}9&7&5\\0&12&0\\-1&-5&-3\end{vmatrix}$

$=|12(-27+5)|=264$ cubic units