Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 11 - Vectors and the Geometry of Space - 11.7 Exercises - Page 809: 38

Answer

$$\left( {0,0,12} \right)$$

Work Step by Step

$$\eqalign{ & \left( {9,\frac{\pi }{4},\pi } \right) \cr & \left( {\rho ,\theta ,\phi } \right):{\text{ }}\left( {9,\frac{\pi }{4},\pi } \right) \to \rho = 9,{\text{ }}\theta = \frac{\pi }{4},{\text{ }}\phi = \pi \cr & {\text{Spherical to rectangular }}\left( {\rho ,\theta ,\phi } \right) \cr & x = \rho \sin \phi \cos \theta ,{\text{ }}y = \rho \sin \phi \sin \theta ,{\text{ }}z = \rho \cos \phi \cr & x = \left( 9 \right)\sin \left( {\frac{\pi }{4}} \right)\cos \left( \pi \right) = - \frac{{9\sqrt 2 }}{2} \cr & y = \left( 9 \right)\sin \left( {\frac{\pi }{4}} \right)\sin \left( \pi \right) = 0 \cr & z = \left( 9 \right)\cos \left( \pi \right) = - 9 \cr & {\text{The rectangular }}\left( {x,y,z} \right){\text{ coordinates are:}} \cr & \left( {0,0,12} \right) \cr} $$
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