Consider a △ A B C △ A B C where A ( 1 , 3 , 2 ) , B ( − 2 , 8 , 0 ) A ( 1 , 3 , 2 ) , B ( − 2 , 8 , 0 ) and C ( 3 , 6 , 7 ) C ( 3 , 6 , 7 ) . If the angle bisector of ∠ B A C ∠ B A C meets the line B C B C at D D , then the length of the projection of the vector AD on the vector AC is:

(1) 37/2√38
(2) √38/2
(3) 39/2√38
(4) √19