## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 782: 57

.

#### Work Step by Step

Vectors are $u={{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j},v={{a}_{2}}\mathbf{i}+{{b}_{2}}\mathbf{j},$ and $w={{a}_{3}}\mathbf{i}+{{b}_{3}}\mathbf{j}$. Now, put these vectors in the expression $u+v=v+u$. Then, \begin{align} & \left( {{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j} \right)+\left( {{a}_{2}}\mathbf{i}+{{b}_{2}}\mathbf{j} \right)=\left( {{a}_{2}}\mathbf{i}+{{b}_{2}}\mathbf{j} \right)+\left( {{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j} \right) \\ & \left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j}=\left( {{a}_{2}}+{{a}_{1}} \right)\mathbf{i}+\left( {{b}_{2}}+{{b}_{1}} \right)\mathbf{j} \\ & \left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j}=\left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j} \\ \end{align} Left side and right side are equal. Hence, $u+v=v+u$.

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.