University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.1 - Three-Dimensional Coordinate Systems - Exercises - Page 599: 24

Answer

$a.\quad $ A plane, perpendicular to the yz plane, intersecting the plane yz in the line $z=1-y.$ $ b.\quad$ The cubic curve $z=y^{3}$ in the plane $x=2$ (which is parallel to the yz plane).

Work Step by Step

$a.\quad $ In the plane $x=0$ (the yz plane),$ z=1-y $ is a line. Translating this line across planes $x=k$ (parallel to the yz plane), a plane is formed, perpendicular to the yz plane, intersecting the plane yz in the line $z=1-y.$ $ b.\quad$ In the plane $x=0$ the equation $z=y^{3}$ is a cubic curve. Translating along the x axis by 2 units, this curve is now in the plane $x=2.$
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