Answer
$1.77$ 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, $p=\lt \sqrt 3,-7,0 \gt$ and $q=\lt \sqrt 3,1,-2 \gt$
$|p|=\sqrt{(\sqrt 3)^2+(-7)^2+(0)^2}= 2 \sqrt {13}$ and $|q|=\sqrt{(\sqrt 3)^2+(1)^2+(-2)^2}=\sqrt {8}$
Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} \dfrac{-4}{ ( 2 \sqrt {13})(\sqrt 8)})=\cos ^{-1} \dfrac{-4}{ 4 \sqrt {26}}$
or, $ \theta \approx 1.77$ rad
