## Precalculus (6th Edition) Blitzer

$\mathbf{v}$ and $\mathbf{w}$ are not orthogonal.
Dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as, \begin{align} & \mathbf{v}\cdot \mathbf{w}=\left( 5\mathbf{i}+0\mathbf{j} \right)\cdot \left( -6\mathbf{i}+0\mathbf{j} \right) \\ & =5\cdot \left( -6 \right)+0\cdot 0 \\ & =-30+0 \\ & =-30 \end{align} As the dot product of $\mathbf{v}$ and $\mathbf{w}$ is not zero, thus, $\mathbf{v}$ and $\mathbf{w}$ are not orthogonal. Hence, $\mathbf{v}$ and $\mathbf{w}$ are not orthogonal.