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, $p=\lt 7,0,0 \gt$ and $q=\lt 1,1,\sqrt 2 \gt$
$|p|=\sqrt{7^2+0^2+0^2}= \sqrt {49}=7$ and $|q|=\sqrt{1^2+1^2+(\sqrt 2)^2}=2$
Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} (\dfrac{7}{ (7)(2)})$
or, $ \theta =\dfrac{\pi}{3}$
