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 783: 80


a) The resultant force is $\text{4}\mathbf{i}-10\mathbf{j}$. b) The additional force required for the given forces to be in equilibrium is $-\text{4}\mathbf{i}+10\mathbf{j}$. $$

Work Step by Step

(a) The given three vectors will be added as follows: $\begin{align} & {{F}_{1}}+{{F}_{\text{2}}}+{{F}_{3}}=-2\mathbf{i}+3\mathbf{j}+\mathbf{i}-\mathbf{j}+5\mathbf{i}-12\mathbf{j} \\ & =4\mathbf{i}-10\mathbf{j} \end{align}$ (b) The given three vectors can be added as follows: $\begin{align} & {{F}_{1}}+{{F}_{\text{2}}}+{{F}_{3}}=-2\mathbf{i}+3\mathbf{j}+\mathbf{i}-\mathbf{j}+5\mathbf{i}-12\mathbf{j} \\ & =4\mathbf{i}-10\mathbf{j} \end{align}$
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