Question

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

Answer 1

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