Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 784: 110


The statement is false.

Work Step by Step

When multiplying a constant $\left( -1 \right)$ with a vector, the direction of the new vector and original vector will be opposite, but magnitude will be same. Hence, the direction of $\mathbf{E}$ and $-\mathbf{E}$ will be opposite but the magnitudes will be the same and similarly for $\mathbf{F}$. From the given graph, the addition of two vectors is $\begin{align} & \mathbf{G}-\mathbf{F}=-\mathbf{A} \\ & \mathbf{B}-\mathbf{E}\ne -\mathbf{A} \\ \end{align}$ Therefore, $\mathbf{B}-\mathbf{E}\ne \mathbf{G}-\mathbf{F}$ Both vectors do not equal in magnitude as well as direction due to which $\left( \mathbf{B}-\mathbf{E} \right)$ and $\left( \mathbf{G}-\mathbf{F} \right)$ are not equal. Thus, the statement is false.
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