## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 13 - Vector Geometry - 13.5 Planes in 3-Space - Exercises - Page 685: 42

#### Answer

$$(9,18,3).$$

#### Work Step by Step

The parametric equations of the line are given by $$x=1+4t, \quad y=9t, \quad z=-1+2t.$$ Now, substituting in the equation of the plane $$x-z=6\Longrightarrow 1+4t+1-2t=6\\ \Longrightarrow 2t=4\Longrightarrow t=2.$$ So the point of intersection is given by $$(9,18,3).$$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.