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: 37

Answer

Direction cosines are: $\frac{1}{\sqrt 3},\frac{1}{\sqrt 3},\frac{1}{\sqrt 3}$ Direction angles are: $55 ^\circ, 55^\circ, 55 ^\circ$

Work Step by Step

Given:$\lt c,c,c \gt$ Direction cosines are: $cos \alpha = \frac{c}{\sqrt {c^2+c^2+c^2}}=\frac {1}{\sqrt 3}, cos \beta =\frac{c}{\sqrt {c^2+c^2+c^2}}=\frac {1}{\sqrt 3}, cos \gamma=\frac{c}{\sqrt {c^2+c^2+c^2}}=\frac {1}{\sqrt 3}$ Thus, the direction angles are: $ \alpha =cos^{-1} \frac {1}{\sqrt 3}=55 ^\circ, \beta = cos^{-1} \frac {1}{\sqrt 3}=55 ^\circ, \gamma = cos^{-1} \frac {1}{\sqrt 3}=55 ^\circ$
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