Calculus (3rd Edition)

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

Chapter 13 - Vector Geometry - 13.7 Cylindrical and Spherical Coordinates - Preliminary Questions - Page 699: 2


(a) The statement is not correct. (b) The statement is correct.

Work Step by Step

In cylinderical coordinates, we have $$ \begin{aligned} &x=r \cos \theta\\ &y=r \sin \theta\\ &z=z \end{aligned} $$ (a) When $\theta =0$, then $x=r, y=0$ and $z=z$. Hence, the statement is not correct. (b) When $\theta =0$, then $x=r, y=0$ and $z=z$. So the point lies on the $xz$-plane. Thus, the statement is correct.
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