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: 54


Neither, $cos^{-1}|\dfrac{-1}{\sqrt {11}}| \approx 95.2 ^{\circ}$

Work Step by Step

$n_1=\lt1,-1,3\gt$ and $n_2=\lt 3,1,-1\gt$ Angle between two vectors$\theta= cos^{-1}|\dfrac{a.b}{|a||b|}|$ $\theta= cos^{-1}|\dfrac{-1}{\sqrt {11} \sqrt {11}}|$ $\theta= cos^{-1}|\dfrac{-1}{\sqrt {11}}|$ $\theta \approx 95.2 ^{\circ}$ Hence, the two planes are neither parallel or perpendicular.
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