向量b-向量a=(cosx-sinx,-3/2)
f(x)=向量a.(向量b-向量a)=sinx(cosx-sinx)+1*(-3/2).
=sinxcosx-sinx^2-3/2.
=(1/2)(2sinxcosx)-sin^2x-3/2.
=(1/2)sin2x-(1/2)cos2x-1/2-3/2.
=(1/2)(sin2x-cos2x)-2.
=(√2/2)sin(2x+π/4)-2.
T=2π/2
∴T=π.----即为所求.