Consider a \(\triangle ABC\) where \(A (1,3,2), B (-2,8,0)\) and \(C (3,6,7)\). If the angle bisector of \(\angle BAC\) …

Consider a \(\triangle ABC\) where \(A (1,3,2), B (-2,8,0)\) and \(C (3,6,7)\). If the angle bisector of \(\angle BAC\) meets the line \(B C\) at \(D\), then the length of the projection of the vector \(\overrightarrow{A D}\) on the vector \(\overrightarrow{A C}\) is :EndFragment

[JEE Main 2024, 01 Feb (Shift 2)]