Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 482: 29

Answer

Since there is a real number $n$ such that the product of $n$ and a direction vector for line 1 is equal to a direction vector of line 2, the two lines are parallel.

Work Step by Step

A direction vector for line 1 is $(1,2,-3)$ A direction vector for line 2 is $(-1,-2,3)$ Note that $(-1) \cdot (1,2,-3) = (-1,-2, 3)$ Since there is a real number $n$ such that the product of $n$ and a direction vector for line 1 is equal to a direction vector of line 2, the two lines are parallel.
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