## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.6 - Vectors - Concept and Vocabulary Check - Page 781: 5

#### Answer

The vector that appears to be a scalar multiple of $\mathbf{v}$ is $\mathbf{w}$, where the scalar is negative.

#### Work Step by Step

The scalar multiples of $\mathbf{v}$ are the vectors $\mathbf{w}$, $\mathbf{a}$, and $\mathbf{b}$. The vector $\mathbf{w}$ is a negative scalar multiple of $\mathbf{v}$, because it is anti parallel with $\mathbf{v}$. The vector $\mathbf{a}$ is a positive scalar multiple of $\mathbf{v}$ because it is parallel with $\mathbf{v}$. The vector $\mathbf{b}$ is also a positive scalar multiple of $\mathbf{v}$, because it is parallel with $\mathbf{v}$, and its length is also the same as vector $\mathbf{v}$, so its scalar multiple is 1. Therefore, the vector that appears to be a scalar multiple of v is $\mathbf{w}$, where the scalar is negative.

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