Answer
The vectors $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
Work Step by Step
Dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as,
$\begin{align}
& \mathbf{v}\cdot \mathbf{w}=\left( -2\mathbf{i}+3\mathbf{j} \right)\cdot \left( -6\mathbf{i}-4\mathbf{j} \right) \\
& =\left( -2 \right)\cdot \left( -6 \right)+3\cdot \left( -4 \right) \\
& =12-12 \\
& =0
\end{align}$
Since, the dot product of $\mathbf{v}$ and $\mathbf{w}$ is $0$, thus $\mathbf{v}$ and $\mathbf{w}$ are orthogonal vectors.
Hence, $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
