Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 9 - Polar Coordinates; Vectors - 9.4 Vectors - 9.4 Assess Your Understanding - Page 606: 47



Work Step by Step

We know that if $k=ai+bj$ and $l=ci+dj$, then $k+l=(a+c)i+(b+d)j$ and that if $z$ is a constant, then $zk=(za)i+(zb)j$. Also, the magnitude of a vector $v=ai+bj$ is: $||v||=\sqrt{a^2+b^2}$. Hence here: $||v||-||w||=||(3i-5j)||-||(-2i+3j)||=\sqrt{3^2+(-5)^2}-\sqrt{(-2)^2+3^2}=\sqrt{9+25}-\sqrt{4+9}=\sqrt{34}-\sqrt{13}.$
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