Question

向量e1,向量e2是两个不共线的向量，且向量AB=2向量e1+k向量e2，向量CB=2向量e1-3向量e2

若A,B,D三点共线，则K的值为？

Answer 1

AB=2e1+ke2 (1)
CB=2e1-3e2 (2)
若A,B,C三点共线
=> AB = mCB ( m is a constant)
2e1+ke2=m(2e1-3e2)
=>
2=2m and k=-3m
=>m=1 and k=-3m
=>k=-3