Question:

The position vectors of points $\displaystyle A$ and $\displaystyle B$ are $\displaystyle \left(\begin{array}{c}-3\\6\\3\end{array}\right)$ and $\displaystyle \left(\begin{array}{c}-1\\2\\4\end{array}\right)$ respectively, relative to an origin $\displaystyle O$.

(i) Calculate angel AOB.

(ii) The point C is such that $\displaystyle \vec{AC} = 3\vec{AB}$. Find the unit vector in the direction of $\displaystyle \vec{OC}$.

Attempt:

(i) $\displaystyle \theta = 36.7^o$

(ii) Need help!