Question

已知向量e1,e2是平面内两个不共线的向量,向量AB=2e1+e2,向量BE=-e1+xe2,EC=-2e1+e2,且A

Answer 1

A,E,C三点共线

let

|AE|/|EC|=k

BE = (BA+kBC)/(1+k)

=(-AB+k(BE+EC)/(1+k)

BE=(-AB+kEC)

-e1+xe2 = (-2e1-e2+ k(-2e1+e2) )

(1+2k)e1+(x+1+k)e2=0

=>

1+2k= 0 and (x+1+k)=0

k=-1/2 and (x+1+k)=0

=> x+1-1/2=0

x=-1/2