Answer
$\dfrac{\pi}{3}$
Work Step by Step
Formula to calculate the angle between two plane vectors $a$ and $b$ is defined as:
$ \theta = \cos ^{-1} (\dfrac{a \cdot b}{|a||b|})$
Here, $a=\lt 7,0,0 \gt$ and $b=\lt 1,1,\sqrt 2 \gt$
$|a|=\sqrt{7^2+0^2+0^2}= \sqrt {49}=7$ and $|b|=\sqrt{1^2+1^2+(\sqrt 2)^2}=2$
Hence, $ \theta =\cos ^{-1} (\dfrac{7}{ (7)(2)})=\dfrac{\pi}{3}$
