Find the volume of the parallelepiped with vertices (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6).



\(\text{Let $\vec{a}=\begin{pmatrix}0\\5\\1 \end{pmatrix}$ } \quad \text{Let $\vec{b}=\begin{pmatrix}3\\0\\0 \end{pmatrix}$ } \quad \text{Let $\vec{c}=\begin{pmatrix}2\\0\\5 \end{pmatrix}$ } \)
\(\begin{array}{|rcll|} \hline \mathbf{V} &=& \left| \begin{vmatrix}0&3&2\\5&0&0\\1&0&5 \end{vmatrix}\right| \\ &=& \left| 0 - 3\cdot \begin{vmatrix}5&0\\1&5 \end{vmatrix} +0 \right| \\ &=& \left| -3\cdot 25 \right| \\ &=& \left| -75 \right| \\ &=& \mathbf{75} \\ \hline \end{array}\)
