## Precalculus (6th Edition) Blitzer

The vectors $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
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.