# Chapter 11 - Practice Exercises - Page 638: 42

$\dfrac{\pi}{3}$

#### Work Step by Step

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

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