## Precalculus (6th Edition) Blitzer

$\mathbf{v}$ 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+}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.