Question

设向量e1,向量e2是平面上一组基底,

Answer 1

AB=e1+e2,BC=2e1+8e2,CD=3(e1-e2)

(1)

BD = CD+CD= 5e1+5e2 = 5(e1+e2) = 5AB

=> AB//BD

=> A,B,D 三点共线

(3)

AB=2e1+ke2,CB=e1+3e2,CD=2e1-e2

BD = BC +CD = e1-4e2

A、B、D共线

=> AB = mBD

2e1+ke2 = m(e1-4e2)

=> 2 = m and k =-4m

=> k=-8