Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 782: 60


See the explanation below.

Work Step by Step

Vectors are $u={{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j}$. Now, put vector $u$ in the expression $\left( c+d \right)u=cu+du$. Then, we get $\begin{align} & \left( c+d \right)\left( {{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j} \right)=c\left( {{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j} \right)+d\left( {{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j} \right) \\ & c{{a}_{1}}\mathbf{i}+c{{b}_{1}}\mathbf{i}+d{{a}_{1}}\mathbf{i}+d{{b}_{1}}\mathbf{j}=c{{a}_{1}}\mathbf{i}+c{{b}_{1}}\mathbf{j}+d{{a}_{1}}\mathbf{i}+d{{b}_{1}}\mathbf{j} \end{align}$ Left side and right side are equal. Hence, $\left( c+d \right)u=cu+du$.
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