Answer
$\frac{7\pi}{12} rad=105^\circ$
Work Step by Step
$\mathbf{u}=\cos\left(\frac{\pi}{6}\right)\mathbf{i}+\sin\left(\frac{\pi}{6}\right)\mathbf{j}\hspace{10mm}\mathbf{v}=\cos\left(\frac{3\pi}{4}\right)\mathbf{i}+\sin\left(\frac{3\pi}{4}\right)\mathbf{j}$
We can solve this problem without even using the dot product. These two vectors point to points on the unit circle. $\mathbf{u}$ points to the polar coordinate $(1,\frac{\pi}{6})$, and $\mathbf{v}$ points to the polar coordinate $(1,\frac{3\pi}{4}).$ The angle between the two vectors is therefore $\frac{3\pi}{4}-\frac{\pi}{6}=\frac{7\pi}{12}=105^\circ$
