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High School Mathematics-Vector: A Problem to Be Solved
I am here to provide a general analysis method.

Establish a plane rectangular coordinate system, with the center of the regular hexagon as the origin, FC as the X axis and vertical FC as the Y axis.

Let c coordinate be (1 0), F(- 1 0), B( 1/2, √3/2), A(- 1/2, √3/2) and d (6544).

Vector BF=(-3/2, -√3/2), FD=(3/2, -√3/2),

BM= √3/3BF,FN=√3/3FD,BM=(-√3/2,- 1/2),FN=(√3/2,- 1/2)

Get the m coordinates (1/2-√3/2, √3/2- 1/2) and the n coordinates (√3/2- 1,-1/2).

AM=( 1-√3/2,- 1/2),AN=(√3/2- 1/2,- 1/2-√3/2)

AM=(√3- 1)/2AN, which means AMN three-point * * * line.