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: 10


a) $=(\frac{1}{\sqrt 2},-\frac{1}{\sqrt 2})$ b) $=(-\frac{1}{\sqrt 2},\frac{1}{\sqrt 2})$

Work Step by Step

a) The magnitude of this vector is given by $\sqrt {(1)^{2} +(-1)^{2}}=\sqrt 2$. Therefore a unit vector in direction $u$ is given by: $\frac{1}{\sqrt 2}(1,-1)$ $=(\frac{1}{\sqrt 2},-\frac{1}{\sqrt 2})$ 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 $(-1)\times(\frac{1}{\sqrt 2},-\frac{1}{\sqrt 2})$ $=(-\frac{1}{\sqrt 2},\frac{1}{\sqrt 2})$
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