As shown in the figure, the edge length of cube abcd-a1b1c1d1 is 4, M is the midpoint of BD1, n is on a1c1, and | A1N | = 3 | NC1 |, then the length of Mn is___ ． | Math enthusiast | Mathematical art

As shown in the figure, the edge length of cube abcd-a1b1c1d1 is 4, M is the midpoint of BD1, n is on a1c1, and | A1N | = 3 | NC1 |, then the length of Mn is___ ．

Take D as the vertex, the line where Da is located is the x-axis, the line where DC is located is the y-axis, and the line where dd1 is located is the z-axis, as shown in the figure: the edge length of cube abcd-a1b1c1d1 is 4, A1 (4, 0, 4), B (4, 4, 0), C1 (0, 4, 4), M is the midpoint of BD1, so m (2, 2, 2); n is on a1c1, and | A1N | = 3 | NC1

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