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: 34


Direction cosines are: $\frac{6}{7}, \frac{3}{7}, \frac{-2}{7}$ Direction angles are: $31 ^\circ, 65 ^\circ, 107 ^\circ$

Work Step by Step

Let $v= \lt 6,3,-2 \gt$ $|v|=\sqrt {6^2+3^2+(-2)^2}=7$ Direction cosines are: $cos \alpha = \frac{6}{7}, cos \beta =\frac{3}{7}, cos \gamma=\frac{-2}{7}$ Thus, the direction angles are: $ \alpha =cos^{-1} \frac{6}{7}=31 ^\circ, \beta = cos^{-1} \frac{3}{7}=65 ^\circ, \gamma = cos^{-1} \frac{-2}{7}=107^ \circ$
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