Answer
$\mathbf{v}=4\sqrt{2}\mathbf{i}+4\sqrt{2}\mathbf{j}$
Work Step by Step
Therefore,
$\begin{align}
& \mathbf{v}=\parallel v\parallel \cos {{45}^{\circ }}\mathbf{i}+\parallel v\parallel \sin {{45}^{\circ }}\mathbf{j} \\
& =\left( 8\times \frac{1}{\sqrt{2}} \right)\mathbf{i}+\left( 8\times \frac{1}{\sqrt{2}} \right)\mathbf{j} \\
& =4\sqrt{2}\mathbf{i}+4\sqrt{2}\mathbf{j}
\end{align}$
