Chapter 11 - Section 11.5 - Lines and Planes in Space - Exercises - Page 631: 51

$0.82$ rad

The formula to calculate the angle between two planes is: $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})$ Here, $p=\lt 2,2,-1 \gt$ and $q=\lt 1,2,1 \gt$ $|p|=\sqrt{2^2+2^2+(-1)^2}= 3$ and $|q|=\sqrt{1^2+2^2+1^2}=\sqrt 6$ Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} (\dfrac{5}{ 3 \sqrt 6})$ or, $ \theta =0.82$