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: 32



Work Step by Step

Form an equation using the distance formula (distance from (0,0,0) to (x,y,z))=(distance from (0,2,0) to (x,y,z)) $\sqrt{x^{2}+y^{2}+z^{2}}=\sqrt{x^{2}+(y-2)^{2}+z^{2}}\quad $ ... square both sides $x^{2}+y^{2}+z^{2}=x^{2}+(y-2)^{2}+z^{2}\quad $ ... simplify $y^{2}=y^{2}-4y+4$ $4y=4$ $y=1$ (the plane parallel to the xz plane, containing (0,1,0)).
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