Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.5 Equations of Lines and Planes - 12.5 Exercises - Page 872: 67


$P_2$ and $P_3$ are parallel; $P_1$ and $P_4$ are identical .

Work Step by Step

Two planes are parallel when their normal vectors are parallel. From the give problem,, we see that $P_1$ has a normal vector $\lt 3,6,-3\gt$ or $3\lt 1,2,-1\gt $and $P_4$ has normal vectors $\lt 1,2,-1\gt $are identical because they are multiples of each other. $P_2$ has normal vectors $\lt 4,-12,8\gt $ and $P_4$ has normal vectors $\lt 3,-9,6\gt $ Thus, $P_2$ and $P_3$ are parallel because their normal vectors are in same ratio.
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