已知函数f(x)=向量m·向量n,其中向量m=(sinωx+cosωx,√3cosωx),向量n=(cosωx-sinωx,2sinωx)(ω＞0).若f(x)相邻的对称轴间的距离不小于π/2.

1）
f(x)=向量m·向量n
=（sinωx+cosωx）（cosωx-sinωx）+√3cosωx*2sinωx
=(cos^2ωx-sin^2ωx）+√3sin2ωx
=cos2ωx+√3sin2ωx
=2sin(2ωx+π/6)
相邻的对称轴间的距离=2π/2ω÷2=π/2ω
所以,π/2ω≥π/2
ω≤1
2)
当ω最大时,ω=1
f(x)=2sin(2x+π/6)
f(A)=2sin(2A+π/6)=1
sin(2A+π/6)=1/2
2A+π/6=π/6,或,5π/6
A=0,或,π/3
因为A>0,所以,A=π/3
cosA=(b^2+c^2-a^2)/2bc
=[(b+c)^2-2bc-a^2]/2bc
=[(b+c)^2-a^2]/2bc-2
=(9-3)/2bc-1
=3/bc-1
所以,1/2=3/bc-1
bc=2
△ABC的面积=bcsinA/2
=2sinπ/3 /2
=sinπ/3
=√3/2