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