Answer
$ \dfrac{5\pi}{12}$
Work Step by Step
We know that the angle between two vectors is:
$\theta =\cos^{-1} [ \dfrac{u \cdot v}{||u|| \space ||v|| }]$
Therefore, $u .v=\cos \dfrac{\pi}{3}\cos \dfrac{3\pi}{4}+\sin \dfrac{\pi}{3}\sin \dfrac{3\pi}{4} $ and $||u||=1$ and $||v||=1$
$\cos \theta = [\cos \dfrac{\pi}{3}\cos \dfrac{3\pi}{4}+\sin \dfrac{\pi}{3}\sin \dfrac{3\pi}{4} ]$
or, $= \cos ( \dfrac{\pi}{3}- \dfrac{3\pi}{4} )$
or, $= \cos (- \dfrac{5\pi}{12})$
So, $\theta = \dfrac{5\pi}{12}$
