University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 11 - Practice Exercises - Page 638: 41



Work Step by Step

The formula to calculate the angle between two planes is: $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})$ Here, $p=\lt 7,0,0 \gt$ and $q=\lt 1,1,\sqrt 2 \gt$ $|p|=\sqrt{7^2+0^2+0^2}= \sqrt {49}=7$ and $|q|=\sqrt{1^2+1^2+(\sqrt 2)^2}=2$ Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} (\dfrac{7}{ (7)(2)})$ or, $ \theta =\dfrac{\pi}{3}$
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