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: 12


a) $=(-\frac{1}{\sqrt {26}},\frac{3}{\sqrt {26}}, \frac{4}{\sqrt {26}})$ b) $=(\frac{1}{\sqrt {26}},-\frac{3}{\sqrt {26}}, -\frac{4}{\sqrt {26}})$

Work Step by Step

a) The magnitude of this vector is given by $\sqrt {(-1)^{2} +(3)^{2}+(4)^{2}}=\sqrt {26}$. Therefore a unit vector in direction $u$ is given by: $\frac{1}{\sqrt {26}}(1,3,4)$ $=(-\frac{1}{\sqrt {26}},\frac{3}{\sqrt {26}}, \frac{4}{\sqrt {26}})$ b) a unit vector in the opposite direction is given by multiplying the unit vector found in part a) by $(-1)$ This is equal to $(-1)\times(-\frac{1}{\sqrt {26}},\frac{3}{\sqrt {26}}, \frac{4}{\sqrt {26}})$ $=(\frac{1}{\sqrt {26}},-\frac{3}{\sqrt {26}}, -\frac{4}{\sqrt {26}})$
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