If \(4 \hat{i}+7 \hat{j}+8 \hat{k}, 2 \hat{i}+3 \hat{j}+4 \hat{k}\) and \(2 \hat{i}+5 \hat{j}+7 \hat{k}\) are the position vectors of the vertices \(\mathrm{A}, \mathrm{B}\) and C , respectively, of triangle ABC , then the position vector of the point in which bisector of \(\angle B\) meets \(C A\) is

1. A \(\hat{i}(4 \sqrt{13}+12)+\hat{j}(7 \sqrt{13}+30)+\hat{k}(8 \sqrt{3}+42)\)
2. B \(\frac{\hat{i}(4 \sqrt{13}+12)+\hat{j}(7 \sqrt{13}+30)+\hat{k}(8 \sqrt{13}+42)}{\sqrt{13}-6}\)
3. C \(\frac{\hat{i}(4 \sqrt{13}+12)+\hat{j}(7 \sqrt{13}+30)+\hat{k}(8 \sqrt{13}+42)}{\sqrt{13}+6}\)
4. D \(\frac{\hat{i}(4 \sqrt{13}+12)+\hat{j}(7 \sqrt{13}+30)-\hat{k}(8 \sqrt{13}+42)}{6-\sqrt{13}}\)