Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.1 Vectors in the Plane - Exercises - Page 650: 45


$$u=-\sqrt 2 v=-\sqrt2(i-j).$$

Work Step by Step

The vector $u$ that has length $2$ and in the direction opposite to $v=i-j$ is given by $$u=-av=-a i +aj.$$ To find $a$, we have $$2=\sqrt{a^2+a^2}\Longrightarrow a=\sqrt 2 $$ Hence, $$u=-\sqrt 2 v=-\sqrt2(i-j).$$
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