## Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole

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

#### Answer

$(x,y,z) = (4-n, 1+2n, -3+5n)$

#### Work Step by Step

In general we can write an equation for a line in this form: $(x,y,z) = (a,b,c)+n(a',b',c') = (a+a'n, b+b'n,c+c'n)$ where $(a,b,c)$ is a point on the line and $(a',b',c')$ is a direction vector $(4,1,-3)$ is a point on the line $(-1,2,5)$ is a direction vector Note that parallel lines have the same direction vector. We can write an equation for this line: $(x,y,z) = (4,1,-3)+n(-1,2,5) = (4-n, 1+2n, -3+5n)$

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