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: 23

Answer

This is the plane that intersects the $x$-axis at $x=5$ and is parallel to $yz$-plane.

Work Step by Step

This region is the set of all points $(x,y,z)$ that satisfy the equation $x=5$. So this is the set of all points with $x$-coordinate equal to 5. We know the $yz$-plane is the set of all points $(x,y,z)$ with zero $x$-coordinate, so we can obtain our region by shifting each point in the the $yz$-plane 5 units in the positive $x$-direction. Hence our region is the plane that intersects the $x$-axis at $x=5$ and is parallel to $yz$-plane.
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