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 - 5.2 Inner Product Spaces - 5.2 Exercises - Page 245: 17

Answer

(a) $\langle u, v \rangle =-33$ (b) $\| u \| =5$ (c) $\| v \| =13$ (d) $d(u,v)=\sqrt{260}$

Work Step by Step

$u=(3,4), \quad v=(5,-12)$ (a) $\langle u, v \rangle =u_1v_1+u_1v_2=15-48=-33$ (b) $\| u \| =\sqrt{\langle u, u\rangle}=\sqrt{u_1^2+u_2^2}=\sqrt{9+25}=5$ (c) $\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+v_2^2}=\sqrt{25+144}=13$ (d) $d(u,v)=\| u-v \|=\| (-2,16) \|=\sqrt{4+256}=\sqrt{260}$
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