Answer
$\sqrt {213}$ square units
Work Step by Step
The area of the parallelogram is given as:
$||\textbf{v}\times\textbf{w}||$
We calculate the cross product as follows:
$\textbf{v}\times\textbf{w}=\begin{vmatrix}\textbf{i}&\textbf{j}&\textbf{k}\\1&3&-2\\2&-1&4\end{vmatrix}$
$=\textbf{i}(3\times4-(-1\times-2))-\textbf{j}(1\times4-2\times-2)+\textbf{k}(1\times-1-2\times3)$
$=10\textbf{i}-8\textbf{j}-7\textbf{k}$
$||\textbf{v}\times\textbf{w}||=\sqrt {10^{2}+(-8)^{2}+(-7)^{2}}=\sqrt {213}$
