Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.1 - Three-Dimensional Coordinate Systems - Exercises 12.1 - Page 695: 22

Answer

$a.\quad $the line $x=y$, in the xy-plane $b.\quad $A plane containing points $(t,t,z) $ (the x- and y-coordinates are equal; z can be any number).

Work Step by Step

$a.\quad $ $z=0$ is the xy-plane, and these are the points on the line $x=y$, in the xy-plane. $b.\quad $ When the line from part (a) is raised or lowered at will (when the xy plane is raised or lowered), a plane is formed, perpendicular to the xy-plane, containing the above line. All the points in this plane have coordinates $(t,t,z) $ (the x- and y-coordinates are equal, z can be any number).
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