# Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 792: 27

$\mathbf{v}$ 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( 2\mathbf{i}-2\mathbf{j} \right)\cdot \left( -\mathbf{i}+\mathbf{j} \right) \\ & =2\cdot \left( -1 \right)+\left( -2 \right)\cdot 1 \\ & =-2-2 \\ & =-4 \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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