Let $O$ be the origin and the position vectors of $A$ and $B$ be $2\hat{i} + 2\hat{j} + \hat{k}$ and $2\hat{i} + 4\hat{j} + 4\hat{k}$ respectively. If the internal bisector of $\angle AOB$ meets the line $AB$ at $C$, then the length of $OC$ is:
\( \dfrac{3}{2}\sqrt{31} \)
\( \dfrac{3}{2}\sqrt{34} \)
\( \dfrac{2}{3}\sqrt{31} \)
\( \dfrac{2}{3}\sqrt{34} \)
