Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 12 - Vectors and the Geometry of Space - 12.1 Exercises - Page 815: 24

Answer

This is the plane that intersects the $y$-axis at $y=-2$ and is parallel to $xz$-plane.

Work Step by Step

This region is the set of all points $(x,y,z)$ that satisfy the equation $y=-2$. So this is the set of all points with $y$-coordinate equal to -2. We know the $xz$-plane is the set of all points $(x,y,z)$ with zero $y$-coordinate, so we can obtain our region by shifting each point in the the $xz$-plane 2 units in the negative $y$-direction. Hence our region is the plane that intersects the $y$-axis at $y=-2$ and is parallel to $xz$-plane.
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.