If $4\hat{i}+7\hat{j}+8\hat{k},2\hat{i}+3\hat{j}+24and2\hat{i}+5\hat{j}+7\hat{k}$ are the position vectors of the vertices $A,BandC,$ respectively, of triangle $ABC$ , then the position vecrtor of the point where the bisector of angle $A$ meets $BC$ is a. $\frac{2}{3}\left(-6\hat{i}-8\hat{j}-\hat{k}\right)$ b. $\frac{2}{3}\left(6\hat{i}+8\hat{j}+6\hat{k}\right)$ c. $\frac{1}{3}\left(6\hat{i}+13\hat{j}+18\hat{k}\right)$ d. $\frac{1}{3}\left(5\hat{j}+12\hat{k}\right)$

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