Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - Chapter Review Exercises - Page 703: 65

Answer

The equation in rectangular coordinates: $2x-z=0$

Work Step by Step

We have $z = 2r\cos \theta $. In cylindrical coordinates we have $x = r\cos \theta $. So, $z = 2r\cos \theta $ becomes $z=2x$ in rectangular coordinates. We may write this equation as $2x-z=0$ By Theorem 1 of Section 13.5, this is the equation of a plane with normal vector $\left( {2,0, - 1} \right)$ (red arrow in the second figure).
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