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 \( BC \) at \( D \), then the length of the project of the vector \( \overrightarrow{AD} \) on the vector \( \overrightarrow{AC} \) is:
