Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 3 - Vectors and Coordinate Systems - Exercises and Problems: 27

Answer

The required vector is $(0.707~\hat{i}+0.707~\hat{j})$

Work Step by Step

The vector ($\hat{i}+\hat{j}$) points at a $45^{\circ}$ angle above the positive x-axis. The vectors which point in this direction have the form $(k\hat{i}+k\hat{j})$ for some positive constant $k$. We can find $k$ as: $\sqrt{k^2+k^2} = 1$ $\sqrt{2k^2} = 1$ $k = \frac{1}{\sqrt{2}}$ $k = 0.707$ The required vector is $(0.707~\hat{i}+0.707~\hat{j})$.
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