Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 12 - Section 12.1 - Three-Dimensional Coordinate Systems - 12.1 Exercises - Page 797: 36


A plane, passing through all points on the y-axis, that cuts through the xz-plane at a 45 degree angle.

Work Step by Step

Using intuition, create a two-space coordinate plane xz. For every value x, z must be equal. So, on our 2D coordinate plane, we end up with a line that leaves the origin with a slope m=1. In three-space, our 2D coordinate plane is now our xz-plane. Our 2D line transforms into a plane to accommodate all values of y. What was our 2D slope, m=1, can now be seen as all points on the plane meeting the x-axis at a 45 degree angle relative to the origin.
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