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 799: 87



Work Step by Step

Addition and subtraction for the given vectors: $\mathbf{v}={{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j}$ and $\mathbf{w}={{a}_{2}}\mathbf{i}+{{b}_{2}}\mathbf{j}$, we have $\begin{align} & \mathbf{v}+\mathbf{w}=\left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j} \\ & \mathbf{v}-\mathbf{w}=\left( {{a}_{1}}-{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}-{{b}_{2}} \right)\mathbf{j} \\ \end{align}$ Here, ${{a}_{1}}=1,{{a}_{2}}=-2,{{b}_{1}}=-5,{{b}_{2}}=7$. So, $\begin{align} & \mathbf{v}+\mathbf{w}=\left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j} \\ & =\left[ 1+\left( -2 \right) \right]\mathbf{i}+\left( -5+7 \right)\mathbf{j} \\ & =-\mathbf{i}+2\mathbf{j} \end{align}$ Hence, the vector $\mathbf{v}+\mathbf{w}=-\mathbf{i}+2\mathbf{j}$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.