Let the given vectors be: $\vec a= \vec u+ \vec v$ , $\vec b = 2\vec u + \vec v$ , $|\vec u| = 2$ $,|\vec v| = 4$ and angle between vectors $\vec u$ and $\vec v$ is $120^\circ$. Express the unit vector $\vec x$ over vectors $\vec u$ and $\vec v$ if $\vec x$ bisects the angle between vectors $\vec a$ and $\vec b$.
I dont know how to find this unit vector. I know that $\cos(\angle(a,b)) = \dfrac{\vec a\vec b}{|\vec a||\vec b|}$. But I don't know what to do with it. I would appreciate any help.