Answer
$78.9^{\circ}$
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: $\overrightarrow{a} \cdot \overrightarrow{ b}= (-5)(3) +(12) (2) = -15+24=9$
and $|a|=\sqrt {(5)^2+(12)^2}=\sqrt {169}=13 ; |b|=\sqrt {(3)^2+(2)^2}=\sqrt {13}$
Therefore, $ \theta =\cos^{-1} (\dfrac{ 9}{ 13\sqrt {13}})=78.9^{\circ}$
