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: 17


The required value is $\mathbf{v}\cdot \mathbf{w}=-18$.

Work Step by Step

We need $\mathbf{v}\cdot \mathbf{w}$ And, $\begin{align} & \mathbf{v}=-5\mathbf{i}+2\mathbf{j} \\ & \mathbf{w}=2\mathbf{i}-4\mathbf{j} \end{align}$ So, $\begin{align} & \mathbf{v}\cdot \mathbf{w}=\left( -5\mathbf{i}+2\mathbf{j} \right)\cdot \left( 2\mathbf{i}-4\mathbf{j} \right) \\ & =\left( -5\cdot 2 \right)+\left( 2\cdot -4 \right) \\ & =\left( -10 \right)-8 \\ & \mathbf{v}\cdot \mathbf{w}=-18 \end{align}$ So, $\mathbf{v}\cdot \mathbf{w}=-18$ Therefore, the required value is $\mathbf{v}\cdot \mathbf{w}=-18$.
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