已知空间四边形OABC,e.分别是Ab.bc的中点,H是EF上一点且EH=1/3EF.若向量OH=x向量OA+y向量OB+z向量OC,则x.y.z.各为好多

向量OH=OE+EH= OE+1/3EF
= OE+1/3(OF-OE)
=1/3OF+2/3OE
=1/3•1/2(OB+OC)+2/3•1/2(OA+OB)
=1/6(OB+OC)+1/3(OA+OB)
=1/3OA+1/2OB+1/6OC.
X=1/3,y=1/2,z=1/6.