If the position vectors of the vertices A, B and C of a $\Delta $ ABC are respectively $4\widehat i + 7\widehat j + 8\widehat k,$ $2\widehat i + 3\widehat j + 4\widehat k,$ and $2\widehat i + 5\widehat j + 7\widehat k,$ then the position vectors of the point, where the bisector of $\angle $A meets BC is :

Question

${1 \over 2}\left( {4\widehat i + 8\widehat j + 11\widehat k} \right)$

${1 \over 3}\left( {6\widehat i + 11\widehat j + 15\widehat k} \right)$

${1 \over 3}\left( {6\widehat i + 13\widehat j + 18\widehat k} \right)$

${1 \over 4}\left( {8\widehat i + 14\widehat j + 19\widehat k} \right)$

Solution

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