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: 50

Answer

There is no point of intersection.

Work Step by Step

$l: (x,y,z) = (3,-1,7)+r(-5,2,1)$ The x-coordinate on the line has this form: $3-5r$ The y-coordinate on the line has this form: $-1+2r$ The z-coordinate on the line has this form: $7+r$ We can find the value of $r$ such that these three coordinates satisfy the equation of the plane: $2x+3y+4z = 24$ $2(3-5r)+3(-1+2r)+4(7+r) = 24$ $6-10r-3+6r+28+4r = 24$ $31 = 24$ Clearly this statement is a contradiction. Therefore, there is no value of $r$ such that a point on the line satisfies the equation of the plane. Therefore, there is no point of intersection.
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