在△ABC中,∠BAC=90°,AB=6,D在斜边BC上,且CD=2DB,则向量AB·向量AD的值

AB*AD= AB*(AC+CD)
=AB*(AC+(2/3)*CB)
=AB*(AC+(2/3)* (AB -AC))
=AB*[ (1/3)AC + (2/3)*AB]
=(1/3)AB*AC + (2/3)* AB*AB( AB与AC垂直,AB*AC=0)
=(2/3)*6^2
=24