Find the area of the parallelogram with u and v as adjacent edges.
u = 5i -2j
v = 6i -2j
+9519 The area is equal to \(\left|\mathbf{u} \times \mathbf{v}\right|\).
Notice that \(\mathbf{u}\times \mathbf{v} = \det\begin{bmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k}\\5&-2&0\\6&-2&0\end{bmatrix} = \det\begin{bmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k}\\5&-2&0\\1&0&0\end{bmatrix} = 2\mathbf{k}\)
Therefore \(\left|\mathbf{u} \times \mathbf{v}\right| = |2\mathbf{k}| = 2\)
Therefore the area of the required parallelogram is 2 sq. units.
