Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 11 - Three-Dimensional Space; Vectors - 11.6 Planes in 3-Space - Exercises Set 11.6 - Page 819: 22

Answer

True

Work Step by Step

Step 1 1 of 2 We know that parallel planes have parallel normal vectors, and we also know that $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$ represent the unit normal vectors of the $yz$-plane, $xz$-plane and $xy$-plane, respectively. Step 2 2 of 2 Therefore, from the fact that the given plane is parallel to one of the coordinate planes, by the result we mentioned it is clear that the normal vector of this plane needs to be parallel to some of the vectors $\hat{\imath}, \hat{\jmath}, \hat{k}$. The given statement is true!
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