Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 490: 21

Answer

(a) The point $(0,0,6)$ lies in the plane $2x+3y+4z = 24$ (b) The point $(0,3,4)$ does not lie in the plane $2x+3y+4z = 24$ (c) The point $(4,4,1)$ lies in the plane $2x+3y+4z = 24$ (d) The point $(-2,6,3)$ does not lie in the plane $2x+3y+4z = 24$

Work Step by Step

We can verify if the following points lie in the plane $2x+3y+4z = 24$ (a) $(0,0,6)$ $2(0)+3(0)+4(6) = 24$ The point $(0,0,6)$ lies in the plane $2x+3y+4z = 24$ (b) $(0,3,4)$ $2(0)+3(3)+4(4) = 0+9+16 = 25$ The point $(0,3,4)$ does not lie in the plane $2x+3y+4z = 24$ (c) $(4,4,1)$ $2(4)+3(4)+4(1) = 8+12+4 = 24$ The point $(4,4,1)$ lies in the plane $2x+3y+4z = 24$ (d) $(-2,6,3)$ $2(-2)+3(6)+4(3) = -4+18+12 = 26$ The point $(-2,6,3)$ does not lie in the plane $2x+3y+4z = 24$
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