Answer
$\dfrac{\pi}{4}$
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 $q=\lt 2,-1,-2 \gt$
$|p|=\sqrt{1^2+1^2+0^2}=\sqrt 2$ and $|q|=\sqrt{2^2+1^2+(-2)^2}=\sqrt 9=3$
Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} (\dfrac{3}{\sqrt 2 (3)})=\cos ^{-1} (\dfrac{\sqrt 2}{2})$
Hence, $ \theta =\dfrac{\pi}{4}$
