Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.5 Planes in 3-Space - Exercises - Page 684: 11


(b) True. (d) True.

Work Step by Step

The normal vector to the $ yz $-plane is $\langle 1,0,0\rangle $ and using the fact that parallel planes have parallel normal vectors, we have: (a) False, since $\langle 0,0,1\rangle $ is not parallel $\langle 1,0,0\rangle $. (b) True. (c) False, since $\langle 0,a,b\rangle $ is not parallel $\langle 1,0,0\rangle $. (d) True, $ x=d $ has the normal vector $\langle 1,0,0\rangle $.
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