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: 30


$v=-i+3j$ $||v||=\sqrt{10}$

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 $v=\langle x_2-x_1,y_2-y_1\rangle=(x_2-x_1)i+(y_2-y_1)j.$ Hence, here $v=(-1-0)i+(1-(-2))j\\ v=-i+3j$ The magnitude of a vector $v=ai+bj$ is: $||v||=\sqrt{a^2+b^2}$. Thus, $||v||=\sqrt{(-1)^2+3^2}\\ ||v||=\sqrt{1+9}\\ ||v||=\sqrt{10}$
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