Answer
$\dfrac{\pi}{2}$
Work Step by Step
The formula to calculate the angle between two planes is:
$ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})$
Here, $p=\lt 5,1,-1 \gt$ and $q=\lt 1,-2,3 \gt$
$|p|=\sqrt{5^2+1^2+(-1)^2}=\sqrt {27}=3 \sqrt 3$ and $|q|=\sqrt{1^2+(-2)^2+3^2}=\sqrt {14}$
Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} (\dfrac{0}{3 \sqrt 3 (\sqrt {14})})=\cos ^{-1} (0)$
Hence, $ \theta =\dfrac{\pi}{2}$
