## Calculus (3rd Edition)

The volume of the parallelepiped is given as: $|\textbf{u}\cdot (\textbf{v}\times\textbf{w})|$ We calculate the dot product and cross product as follows: $\textbf{u}\cdot (\textbf{v}\times\textbf{w})$= det $\begin{pmatrix}u\\v\\w\end{pmatrix}$ $=\begin{vmatrix}1&2&6\\1&3&-2\\2&-1&4\end{vmatrix}$ $=1(3\times4-(-1\times-2))-2(1\times4-2\times-2)+6(1\times-1-2\times3)$ $=10-16-42=-48$ Volume= $|\textbf{u}\cdot (\textbf{v}\times\textbf{w})|=48$