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 491: 49

Answer

$(x,y,z) = (6,15,-9)$

Work Step by Step

$l: (x,y,z) = (-1,-6,5)+n(1,3,-2)$ The x-coordinate of the line has this form: $-1+n$ The y-coordinate of the line has this form: $-6+3n$ The z-coordinate of the line has this form: $5-2n$ We can find the vale of $n$ such that these three coordinates satisfy the equation of the plane: $2x+3y+z = 48$ $2(-1+n)+3(-6+3n)+(5-2n) = 48$ $-2+2n-18+9n+5-2n = 48$ $9n-15= 48$ $9n= 63$ $n = 7$ We can find the point of intersection: $l: (x,y,z) = (-1,-6,5)+n(1,3,-2)$ $(x,y,z) = (-1,-6,5)+(7)(1,3,-2)$ $(x,y,z) = (-1+7,-6+21,5-14)$ $(x,y,z) = (6,15,-9)$
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