a-b=(1-cosb , sinb-√3)
|a-b|=√[(1-cosb)^2+(sinb-√3)^2]
=√(1-2cosb+cos^2b+sin^2b -2√3sinb +3)
=√[5-4(1/2cosb+√3/2sinb)]
=√[5-4sin(b+π/6)]
当sin(b+π/6)=1时得最小值 √(5-4)=1
当sin(b+π/6)=-1时得最大值√(5+4)=3
∴
1<=|a－b|<=3