Find the area of the parallelogram whose sides are represented by $2\hat{\mathbf{i}}+4\hat{\mathbf{j}}-6\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2\hat{\mathbf{k}}$

$\mathbf{A}\times \mathbf{B}=\left|\begin{array}{ccc}\hat{\mathbf{i}}& \hat{\mathbf{j}}& \hat{\mathbf{k}}\\ 2& 4& -6\\ 1& 0& 2\end{array}\right|$

$$\begin{gathered} =\hat{\mathbf{i}}(8-0)+\hat{\mathbf{j}}(-6-4)+\hat{\mathbf{k}}(0-4) \\ =8\hat{\mathbf{i}}-10\hat{\mathbf{j}}-4\hat{\mathbf{k}} \end{gathered}$$

Area of parallelogram $=|\mathbf{A}\times \mathbf{B}|$

$=\sqrt{(8{)}^2+(10{)}^2+(4{)}^2}$

=13.4 units