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: 30

Answer

The lines intersect at the point $(2,3,4)$

Work Step by Step

When $n=0$, line 1 passes through the point $(2,3,4)$. When $r=0$, line 2 passes through the point $(2,3,4)$. Therefore, the point $(2,3,4)$ is included in each line. A direction vector for line 1 is $(1,2,-3)$ and a direction vector for line 2 is $(2,3,5)$. Since there is no real number $n$ such that the product of $n$ and the direction vector of line 1 is equal to the direction vector of line 2, the lines are not parallel. Therefore, the lines intersect at the point $(2,3,4)$
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