At ⊿ABC, AD=2DB, AE=3EC, CD and BE intersect at F, let vector AB=a, vector AC=b, vector AF=xa+yb, then (x, y) is ().

A.( 1/3, 1/2)? B.( 1/4， 1/3)？ C. (3 July, 3 July) D. (20 September, 2 May)

Analysis: let vector BF=mBE, vector CF=nCD, vector AB=a, vector AC = B.

∴ vector BF=mBE=m(AE-AB)=m(3b/4-a), vector CF=nCD=n(AD-AC)=n(2a/3-b).

The vector af = ab+BF = a+m (3b/4-a) = m3b/4+(1-m) a,

The vector af = AC+cf = b+n (2a/3-b) = n2a/3+(1-n) b.

Compare two vectors

∴3m/4= 1-n； 1-m=2n/3

M=2/3 and n= 1/2 are used to solve two equations simultaneously.

∴ Vector AF= 1/3a+ 1/2b

∴(x,y)=( 1/3, 1/2)

Option a