设∠ABC=x 0则AC=2sinx/sin(2π/3)=4√3/3sinx AB=2sin(π-2π/3-x)/sin(2π/3)=4√3/3sin(π/3-x)向量AB点积向量AC =16/3sinxsin(π/3-x) =16/3sinx(√3/2cosx-1/2sinx) =4√3/3sin(2x)-8/3sin^2(x) =4√3/3sin(2x)-4/3[1+cos(2x)] =8/3[√3/2sin(2x)-1/2cos(2x)]-4/3 =8/3sin(2x-π/6)-4/3∵0∴向量AB点积向量AC的最小值为：8/3sin(-π/6)-4/3=-8/3
