(1)
向量BE=AE-AB
=1/2AC- AB
=1/2b-a.
向量CD=AD-AC
=1/3AB-AC
=1/3a-b.
(2)
向量BO=入向量BE,则BE+EO=入BE,
所以向量EO=(入-1)BE.
向量AO=AE+EO
=1/2b+EO
=1/2b+(入-1)BE.
=1/2b+(入-1)(1/2b-a)
=(1-入)a+入/2b.
设向量CO=μCD,
则向量AO=AC+CO
=b+μCD
=b+μ(1/3a-b)
=μ/3a+(1-μ)b.
综上可知：向量AO=(1-入)a+入/2b=μ/3a+(1-μ)b.
所以1-入=μ/3,入/2=1-μ,
解得入=4/5.