Answer
$\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
Work Step by Step
Dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as
$\begin{align}
& \mathbf{v}\cdot \mathbf{w}=\left( 2\mathbf{i+}8\mathbf{j} \right)\cdot \left( 4\mathbf{i}-\mathbf{j} \right) \\
& =2\cdot 4+8\cdot \left( -1 \right) \\
& =8-8 \\
& =0
\end{align}$
As the dot product of $\mathbf{v}$ and $\mathbf{w}$ is zero, $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
