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: 10



Work Step by Step

Find the scalar, $\mathbf{v}\cdot \left( \mathbf{u+w} \right)$ as, $\begin{align} & \mathbf{v}\cdot \left( \mathbf{u+w} \right)\mathbf{=}\left( 3\mathbf{i+j} \right)\cdot \left( 2\mathbf{i-j+i+}4\mathbf{j} \right) \\ & =\left( 3\mathbf{i}+\mathbf{j} \right)\cdot \left( 3\mathbf{i}+3\mathbf{j} \right) \\ & =3\cdot 3\mathbf{+}1\cdot 3 \\ & =9+3 \end{align}$ Solve ahead to get the result as, $\begin{align} & \mathbf{v}\cdot \left( \mathbf{u+w} \right)=9+3 \\ & =12 \end{align}$ Hence, the scalar of $\mathbf{v}\cdot \left( \mathbf{u+w} \right)$ is $12$.
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