Question

在正三角形ABC的边长为1,向量AD=向量DB,向量AE=2向量EC,则向量BE乘以向量CD=？

Answer 1

BE=AE-AB
=2AC/3-AB
CD=AD-AC
=AB/2-AC
故：BE·CD=(2AC/3-AB)·(AB/2-AC)
=-|AB|^2/2-2|AC|^2/3+4AB·AC/3
=-1/2-2/3+(4/3)cosA
=-1/2-2/3+2/3
=-1/2