Answer
$\theta =1.76 rad$
Work Step by Step
The formula to calculate the angle between two planes is:
$ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})$
Here, $p=\lt 2,2,2 \gt$ and $q=\lt 2,-2,-1 \gt$
$|p|=\sqrt{2^2+2^2+2^2}=2 \sqrt 3$ and $|q|=\sqrt{2^2+(-2)^2+(-1)^2}=\sqrt 9=3$
Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} (\dfrac{3}{ 2\sqrt 3 (3)})=\cos ^{-1} (\dfrac{-1}{ 3\sqrt 3})$
or, $\theta =1.76 rad$
Our acute angle will be: $3.14 -1.76=1.38$ rad
