在△ABC中,向量BD=1/2DC,AE=3ED,若AB=a,AC=b试用基底﹛a,b﹜表示向量BE

问题描述:

在△ABC中,向量BD=1/2DC,AE=3ED,若AB=a,AC=b试用基底﹛a,b﹜表示向量BE

AE=3ED,则 AE=3/4AD.
BD=1/2DC, 则BD=1/3BC.
向量BE=AE-AB
=3/4AD-AB
=3/4(AB+BD) -AB
=3/4[AB+1/3BC] -AB
=3/4[AB+1/3(AC-AB)] -AB
=3/4[2/3AB+1/3AC] -AB
=1/2AB+1/4AC -AB
=-1/2AB+1/4AC
=-1/2a+1/4b.