JEE Math Practice Question

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 $$\angle \mathrm{AOB}$$ meets the line $$\mathrm{AB}$$ at $$\mathrm{C}$$, then the length of $$O C$$ is

1. A.$$\frac{3}{2} \sqrt{34}$$
2. B.$$\frac{2}{3} \sqrt{31}$$
3. C.$$\frac{2}{3} \sqrt{34}$$
4. D.$$\frac{3}{2} \sqrt{31}$$