Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.5 Planes in 3-Space - Exercises - Page 685: 54



Work Step by Step

Let the equation of any plane that intersects the $ xy $-plane in the line $ r(t)=t\langle 2,1,0\rangle $ be given by $$ ax+by+cz=d.$$ Now, to find the $ xy $ intersection, we put $ z=0$ and hence we get $$ ax+ by=d.$$ Due to the intersection, we have $$ a=2t, \quad b=t .$$ So the equation of any plane whose intersection with the $ xy $-plane is the line $ r(t)=t\langle 2,1,0\rangle $ is given by $$2tx+ty+cz=d.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.