(1)
向量a=(cosωx-sinωx,sinωx),
b=(-cosωx-sinωx,2√3cosωx),
f(x)=a●b+λ
=sin²ωx-cos²ωx+2√3sinωxcosωx+λ
=√3sin2ωx-cos2ωx+λ
=2(√3/2sin2ωx-1/2cos2ωx)+λ
=2sin(2ωx-π/6)+λ
∵f(x)图像关于直线x=π对称
∴f(π)=2sin(2ωπ-π/6)+λ为最值
∴2ωπ-π/6=kπ+π/2,k∈Z
∴ω=k/2+1/3,k∈Z
∵∈(1/2,1)
∴取k=1得ω=5/6
∴f(x)最小正周期T=2π/(2ω)=6π/5
(2)
y=f（x）的图像经过点(π/4,0)
∴f(π/4)=2sin(5/3*π/4-π/6)+λ=0
∴λ=-2sinπ/4=-√2
f(x) =2sin(5/3x-π/6)-√2
∵x∈[0,3π/5]
∴5/3x∈[0,π]
∴-π/6≤5/3x-π/6≤5π/6
∴ -1/2≤ sin(5/3x-π/6)≤1
∴f(x)的值域为[-1-√2,2-√2]