Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 12 - Section 12.2 - Vectors - 12.2 Exercises - Page 805: 24


$\frac{1}{\sqrt{35}}\langle-5,3,-1\rangle$ is a unit vector in the same direction as $\langle-5,3,-1\rangle$.

Work Step by Step

We are given the vector $\langle-5,3,-1\rangle$. In order to get a unit vector with the same direction, we can simply divide by the length of the vector: $|\langle-5,3,-1\rangle|=\sqrt{(-5)^2+(3)^2+(-1)^2}=\sqrt{35}\Rightarrow \frac{1}{\sqrt{35}}\langle-5,3,-1\rangle$.
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