Answer
$\dfrac{\pi}{3}$
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}$
