## Precalculus (6th Edition) Blitzer

The vectors $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
The dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as, \begin{align} & \mathbf{v}\cdot \mathbf{w}=\left( 3\mathbf{i}-5\mathbf{j} \right)\cdot \left( 6\mathbf{i}+\frac{18}{5}\mathbf{j} \right) \\ & =3\cdot 6+\left( -5 \right)\cdot \frac{18}{5} \\ & =18-18 \\ & =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.