Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 482: 22

Answer

(a) The point $(0,0,10)$ does not lie in the plane $2x+y-z = 10$ (b) The point $(5,3,-3)$ does not lie in the plane $2x+y-z = 10$ (c) The point $(2,4,-2)$ lies in the plane $2x+y-z = 10$ (d) The point $(-3,6,-10)$ lies in the plane $2x+y-z = 10$

Work Step by Step

We can verify if the following points lie in the plane $2x+y-z = 10$ (a) $(0,0,10)$ $2(0)+(0)-(10) = -10$ The point $(0,0,10)$ does not lie in the plane $2x+y-z = 10$ (b) $(5,3,-3)$ $2(5)+(3)-(-3) = 10+3+3 = 16$ The point $(5,3,-3)$ does not lie in the plane $2x+y-z = 10$ (c) $(2,4,-2)$ $2(2)+(4)-(-2) = 4+4+2 = 10$ The point $(2,4,-2)$ lies in the plane $2x+y-z = 10$ (d) $(-3,6,-10)$ $2(-3)+(6)-(-10) = -6+6+10 = 10$ The point $(-3,6,-10)$ lies in the plane $2x+y-z = 10$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.