University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 11 - Section 11.5 - Lines and Planes in Space - Exercises - Page 631: 48

Answer

$\dfrac{\pi}{2}$

Work Step by Step

The formula to calculate the angle between two planes is: $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})$ Here, $p=\lt 5,1,-1 \gt$ and $q=\lt 1,-2,3 \gt$ $|p|=\sqrt{5^2+1^2+(-1)^2}=\sqrt {27}=3 \sqrt 3$ and $|q|=\sqrt{1^2+(-2)^2+3^2}=\sqrt {14}$ Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} (\dfrac{0}{3 \sqrt 3 (\sqrt {14})})=\cos ^{-1} (0)$ Hence, $ \theta =\dfrac{\pi}{2}$
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