Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 482: 34


The two lines are perpendicular.

Work Step by Step

$l_1: (x,y,z) = (1,-2,5)+n(4,1,-3)$ The direction vector is $(a,b,c) = (4,1,-3)$ $l_2: (x,y,z) = (1,-2,5)+r(-3,6,-2)$ The direction vector is $(d,e,f) = (-3,6,-2)$ We can verify the condition stated in the theorem: $ad+be+cf = (4)(-3)+(1)(6)+(-3)(-2)$ $ad+be+cf = (-12)+(6)+(6)$ $ad+be+cf = 0$ Since the direction vectors of the two lines satisfy the condition stated in the theorem, the two lines are perpendicular.
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