Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.1 - Three-Dimensional Coordinate Systems - Exercises 12.1 - Page 696: 60


a) $z $ ; b) $x$; c) $y$

Work Step by Step

The distance between two points can be calculated as: $\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}$ a) Distance from point $P(x,y,z)$ to the xy-plane $(x,y,0)$ : $\sqrt{(x-x)^2+(y-y)^2+(z-0)^2}=\sqrt{z^2}=z$ b) Distance from point $P(x,y,z)$ to the yz-plane $0x,y,z)$ is : $\sqrt{(x-0)^2+(y-y)^2+(z-z)^2}=\sqrt{x^2}=x$ c) Distance from point $P(x,y,z)$ to the zx-plane$(x,0,z)$ is: $\sqrt{(x-x)^2+(y-0)^2+(z-z)^2}=\sqrt{y^2}=y$
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