## Calculus (3rd Edition)

$\sqrt {35}$
The area of the parallelogram is calculated as: $||\textbf{u}\times\textbf{v}||$ We take the cross product: $\textbf{u}\times\textbf{v}=\begin{vmatrix}\textbf{i}&\textbf{j}&\textbf{k}\\1&0&3\\2&1&1\end{vmatrix}$ $=\textbf{i}(0\times1-3\times1)-\textbf{j}(1\times1-3\times2)+\textbf{k}(1\times1-0\times2)$ $=-3\textbf{i}+5\textbf{j}+\textbf{k}$ $||\textbf{u}\times\textbf{v}||=\sqrt {(-3)^{2}+5^{2}+1^{2}}=\sqrt {35}$