Precalculus (10th Edition)

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

Chapter 9 - Polar Coordinates; Vectors - Chapter Review - Review Exercises - Page 635: 29


$v=2i-4j$ $||v||=2\sqrt5$

Work Step by Step

If a vector $v$ initiates at point $P(x_1,y_1)$ and terminates at $Q(x_2,y_2)$ then $v==(x_2-x_1)i+(y_2-y_1)j.$ Hence, here $v=(3-1)i+[-6-(-2)]j\\ v=2i-4j$ The magnitude of a vector $v=ai+bj$ is: $||v||=\sqrt{a^2+b^2}$. Thus, $||v||=\sqrt{2^2+(-4)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt5$
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