Elementary Geometry for College Students (7th Edition)

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 490: 7


(a) $(2,4,5)$ is a point on the line. (b) $\langle 3,-5,2 \rangle$ is a direction vector

Work Step by Step

$(x,y,z) = (2+3n,4-5n,5+2n)$ $(x,y,z) = (2,4,5)+n(3,-5,2)$ (a) We can find a point on the line: When we let $n=0$, $(x,y,z) = (2,4,5)$ Therefore, $(2,4,5)$ is a point on the line. (b) We can let $n=1$ to find a direction vector: $\langle 3,-5,2 \rangle$ is a direction vector
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