Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 12 - Section 12.5 - Equations of Lines and Planes - 12.5 Exercises - Page 832: 53

Answer

Neither, $cos^{-1}|\dfrac{-1}{\sqrt {6}}| \approx 114.1 ^{\circ}$

Work Step by Step

$n_1=\lt1,2,-1\gt$ and $n_2=\lt 2,-2,1\gt$ Angle between two vectors: $\theta= cos^{-1}|\dfrac{a.b}{|a||b|}|$ $\theta= cos^{-1}|\dfrac{-3}{\sqrt {6} \sqrt {9}}|$ $\theta= cos^{-1}|\dfrac{-1}{\sqrt {6}}|$ $\theta \approx 114.1 ^{\circ}$ Hence, the two planes are neither parallel nor perpendicular.
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