Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 792: 25


$\mathbf{v}$ and $\mathbf{w}$ are orthogonal.

Work Step by Step

Dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as $\begin{align} & \mathbf{v}\cdot \mathbf{w}=\left( 2\mathbf{i+}8\mathbf{j} \right)\cdot \left( 4\mathbf{i}-\mathbf{j} \right) \\ & =2\cdot 4+8\cdot \left( -1 \right) \\ & =8-8 \\ & =0 \end{align}$ As the dot product of $\mathbf{v}$ and $\mathbf{w}$ is zero, $\mathbf{v}$ and $\mathbf{w}$ are orthogonal.
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