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: 25

Answer

As a result $\frac{1}{9}\langle8,-1,4\rangle$ is a unit vector in the direction of $\langle8,-1,4\rangle$.

Work Step by Step

We are given the vector $\langle8,-1,4\rangle$. In order to get a unit vector with the same direction we can simply divide by the length of the vector: $|\langle8,-1,4\rangle|=\sqrt{(8)^2+(-1)^2+(4)^2}=\sqrt{81}=9\Rightarrow\frac{1}{9}\langle8,-1,4\rangle$
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