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: 26

Answer

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

Work Step by Step

Dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as, $\begin{align} & \mathbf{v}\cdot \mathbf{w}=\left( 8\mathbf{i}-4\mathbf{j} \right)\cdot \left( -6\mathbf{i}-12\mathbf{j} \right) \\ & =8\cdot \left( -6 \right)+\left( -4 \right)\cdot \left( -12 \right) \\ & =-48+48 \\ & =0 \end{align}$ 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.
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