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: 9



Work Step by Step

Find the scalar, $\mathbf{u}\cdot \left( \mathbf{v+w} \right)$ as, $\begin{align} & \mathbf{u}\cdot \left( \mathbf{v+w} \right)\mathbf{=}\left( 2\mathbf{i-j} \right)\cdot \left( 3\mathbf{i+j+i+}4\mathbf{j} \right) \\ & =\left( 2\mathbf{i-j} \right)\cdot \left( 4\mathbf{i+}5\mathbf{j} \right) \\ & =2\cdot 4+\left( -1 \right)\cdot 5 \\ & =8-5 \end{align}$ Solve further to get the result as, $\begin{align} & \mathbf{u}\cdot \left( \mathbf{v+w} \right)=8-5 \\ & =3 \end{align}$ Hence, the scalar of $\mathbf{u}\cdot \left( \mathbf{v+w} \right)$ is $3$.
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