Answer
$36.87^{\circ}$
Work Step by Step
To obtain the angle $\theta$ between two non-zero vectors $a$ and $b$, we will use the following formula such as:
$ \theta =\cos^{-1} (\dfrac{\overrightarrow{a} \cdot \overrightarrow{ b} }{|a| |b|})$
We have: $\overrightarrow{a} \cdot \overrightarrow{ b}= (1)(1) +(7) (1) =8$
and $|a|=\sqrt {1^1+7^1}=\sqrt {50} ; |b|=\sqrt {(1)^1+(1)^1}=\sqrt {2}$
Therefore, $ \theta =\cos^{-1} (\dfrac{8 }{\sqrt {50} \sqrt {2}})$
and $\theta =\cos^{-1} (\dfrac{8 }{10})=36.87^{\circ}$
