Precalculus (6th Edition) Blitzer

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

Chapter 6 - Test - Page 800: 16


The required value is $3\text{v-4w}=\text{-23i}+\text{22j}$

Work Step by Step

We need: $3\mathbf{v}-4\mathbf{w}$ And, $\begin{align} & \mathbf{v}=-5\mathbf{i}+2\mathbf{j} \\ & \mathbf{w}=2\mathbf{i}-4\mathbf{j} \end{align}$ So, $\begin{align} & 3\text{v-4w}=\text{3}\left( \text{-5i}+\text{2i} \right)-\text{4}\left( \text{2i}-\text{4j} \right) \\ & =\left( -\text{15}-\text{8} \right)\text{i}+\left( \text{6}+\text{16} \right)\text{j} \\ & =\text{-23i}+\text{22j} \end{align}$ So, $3\text{v-4w}=\text{-23i}+\text{22j}$ Therefore, the required value is $3\text{v-4w}=\text{-23i}+\text{22j}$.
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