JEE Advanced 2023 Mathematics question
Let be the cube with the set of vertices . Let be the set of all twelve lines containing the diagonals of the six faces of the cube . Let be the set of all four lines containing the main diagonals of the cube ; for instance, the line passing through the vertices and is in . For lines and , let denote the shortest distance between them. Then the maximum value of , as varies over and varies over , is
Answer: (A)
Solution
By symmetry take the main diagonal through with direction . Face diagonals that meet it give distance 0. A skew face diagonal, e.g. through and with direction : $ n =
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