University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.3 - The Dot Product - Exercises - Page 616: 9

Answer

$0.75$ rad

Work Step by Step

The formula to calculate the angle between two planes is: $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})$ Here, $p=\lt 2,1,0 \gt$ and $q=\lt 1,2,-1 \gt$ $|p|=\sqrt{2^2+1^2+0^2}= \sqrt {5}$ and $|q|=\sqrt{1^2+2^2+(-1)^2}=\sqrt 6$ Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} (\dfrac{4}{ (\sqrt 5)(\sqrt 6)})$ or, $ \theta \approx 0.75$ rad
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