## Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole

# Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 482: 36

#### Answer

(a) $(x,y,z) = (7, -3, 8)$ (b) $(x,y,z) = (-12,16, -11)$

#### Work Step by Step

(a) We can use the line of intersection to find the value of $n$: $(x,y,z) = (-1,5,0) + n(1,-1,1)$ Since $x = 7$, the $x$ coordinate in the line of intersection must be $7$: $-1+n(1) = 7$ $n = 8$ We can use the line of intersection to find the point in both planes: $(x,y,z) = (-1,5,0) + n(1,-1,1)$ $(x,y,z) = (-1,5,0) + (8)(1,-1,1)$ $(x,y,z) = (-1+8,5+(-8),0+8)$ $(x,y,z) = (7, -3, 8)$ (b) We can use the line of intersection to find the value of $n$: $(x,y,z) = (-1,5,0) + n(1,-1,1)$ Since $y = 16$, the $y$ coordinate in the line of intersection must be $16$: $5+n(-1) = 16$ $n = -11$ We can use the line of intersection to find the point in both planes: $(x,y,z) = (-1,5,0) + n(1,-1,1)$ $(x,y,z) = (-1,5,0) + (-11)(1,-1,1)$ $(x,y,z) = (-1-11,5+11,0-11)$ $(x,y,z) = (-12,16, -11)$

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