If \( 4 \hat{\mathbf{j}}+7 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathb...

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If \( 4 \hat{\mathbf{j}}+7 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} \) and \( 2 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+7 \hat{\mathbf{k}} \) are the position vectors of the vertices \( A, B \) and \( C \) respectively of \( \triangle A B C \). The position vector of the :oint where the bisector of \( \angle A \) meets \( B C \) is
(a) \( \frac{1}{3}(6 \hat{\mathbf{i}}+13 \hat{\mathbf{j}}+18 \hat{\mathbf{k}}) \)
(b) \( \left.{ }_{3}^{2} \mathbf{v i}+12 \hat{\mathbf{j}}-8 \hat{\mathbf{k}}\right) \)
(c) \( \frac{1}{3}(-6 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}-9 \hat{\mathbf{k}}) \)
(d) \( \frac{2}{3}(-6 \hat{\mathbf{i}}-12 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}) \)
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