Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 235: 9


a) $=(-\frac{5}{13}, \frac{12}{13})$ b) $=(\frac{5}{13}, -\frac{12}{13})$

Work Step by Step

a) The magnitude of the vector $=\sqrt {(-5)^{2}+(12)^{2}}$ $=\sqrt {169}$ $=13$ Therefore a unit vector in the same direction as $u$ is equal to: $\frac{1}{13}(-5,12)$ $=(-\frac{5}{13}, \frac{12}{13})$. b) The unit vector will go in the opposite direction, if it is multiplied by $-1$. Hence a unit vector going in the opposite direction of $u$ is given by $-1\times (-\frac{5}{13}, \frac{12}{13})$ $=(\frac{5}{13}, -\frac{12}{13})$
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