Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises - Page 853: 33


Direction cosines are: $\frac{2}{3}, \frac{1}{3}, \frac{2}{3}$ Direction angles are: $48 ^\circ,71 ^\circ, 48 ^\circ$

Work Step by Step

Let $v= \lt 2,1,2 \gt$ $|v|=\sqrt {2^2+1^2+2^2}=3$ Direction cosines are: $cos \alpha = \frac{2}{3}, cos \beta =\frac{1}{3}, cos \gamma=\frac{2}{3}$ Thus, the direction angles are: $ \alpha =cos^{-1} \frac{2}{3}=48 ^\circ, \beta = cos^{-1} \frac{1}{3}=71 ^\circ, \gamma = cos^{-1} \frac{2}{3}=48^ \circ$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.