Answer
$\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
Work Step by Step
Dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as,
$\begin{align}
& \mathbf{v}\cdot \mathbf{w}=\left( 8\mathbf{i}-4\mathbf{j} \right)\cdot \left( -6\mathbf{i}-12\mathbf{j} \right) \\
& =8\cdot \left( -6 \right)+\left( -4 \right)\cdot \left( -12 \right) \\
& =-48+48 \\
& =0
\end{align}$
As the dot product of $\mathbf{v}$ and $\mathbf{w}$ is zero, thus, $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
Hence, $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
