Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 792: 29

$\mathbf{v}$ and $\mathbf{w}$ are not orthogonal.

Work Step by Step

Dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as, \begin{align} & \mathbf{v}\cdot \mathbf{w}=\left( 3\mathbf{i}+0\mathbf{j} \right)\cdot \left( -4\mathbf{i}+0\mathbf{j} \right) \\ & =3\cdot \left( -4 \right)+0\cdot 0 \\ & =-12+0 \\ & =-12 \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.

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