(1)、f(x)=向量a*向量b
=√3sinxcosx-cos²x-1/2
=√3/2*sin2x-1/2(2cos²x-1)-1
=√3/2*sin2x-1/2*cos2x-1
=sin(2x-π/6)-1
∵-1≤sin(2x-π/6)≤1
∴-2≤sin(2x-π/6)-1≤0
即函数的最小值为-2
最小正周期为：2π/2=π

(2)、在三角形ABC中
∵f(C)=sin(2C-π/6)-1
=0
∴sin(2C-π/6)=1
即2C-π/6=π/2
解得：C=π/3
又∵ sin (A+C)=sinAcosC+sinCcosA
=1/2*sinA+√3/2*cosA
=2sinA
∴3/2*sinA=√3/2*cosA
即tanA=√3/3
∴A=π/6
则B=π-A-B=π/2
又∵c=3
∴a=√3,b=2√3