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: 36


Direction cosines are: $\frac{1}{3},\frac {2}{3},\frac {2}{3}$ Direction angles are: $70.5 ^\circ, 48.2^\circ, 48.2 ^\circ$

Work Step by Step

Let $v=\frac{1}{2} i+j+k=\lt \frac{1}{2} ,1,1 \gt$ $|v|=\sqrt {(\frac{1}{2} )^2+1^2+1^2}=\frac {3}{2}$ Direction cosines are: $cos \alpha = \frac{\frac {1}{2}}{\frac {3}{2}}=\frac {1}{3}, cos \beta =\frac{1}{\frac {3}{2}}=\frac {2}{3}, cos \gamma=\frac{1}{\frac {3}{2}}=\frac {2}{3}$ Thus, the direction angles are: $ \alpha =cos^{-1} \frac {1}{3}=70.5 ^\circ, \beta = cos^{-1} \frac {2}{3}=48.2^\circ, \gamma = cos^{-1} \frac {2}{3}=48.2^ \circ$
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