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 - Preliminary Questions - Page 684: 3


Not parallel: (c) $ x-y+z=0$.

Work Step by Step

(c) $ x-y+z=0$. Since the normal vector to the given plane is $\langle 1,1,1 \rangle $, then for any parallel plane its normal vector must be in the direction of $\langle 1,1,1 \rangle $. However, the plane in (c) has the normal vector $\langle 1,-1,1 \rangle $, which is not in the direction of $\langle 1,1,1 \rangle $.
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