Answer
$90^{\circ}$
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: $\overrightarrow{a} \cdot \overrightarrow{ b}= (1)(-6) +(2) (3) =-6+6=0$
and $|a|=\sqrt {(1)^2+(2)^2}=\sqrt {5} ; |b|=\sqrt {(-6)^2+(3)^2}=\sqrt { 45}$
Therefore, $ \theta =\cos^{-1} (0)$
and $\theta =\cos^{-1} ( \cos 90^{\circ})=90^{\circ}$
