## 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( \mathbf{i+j} \right)\cdot \left( \mathbf{i-j} \right) \\ & =1\cdot 1+1\left( -1 \right) \\ & =1-1 \\ & =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.