Let Q be the cube with the set of vertices {(x 1 ,x 2 ,x 3 ) 
R 3 : x 1, x 2 ,x 3 {0,1}}. Let F be the set of all twelve lines containing the diagonals of the six faces of the cube Q. Let S be the set of all four lines containing the main diagonals of the cube Q; for instance, the line passing through the vertices (0, 0, 0) and (1, 1, 1) is in S. For lines 
and 
, let 
denote the shortest distance between them. Then the maximum value of 
, as 
varies over F and 
varies over S, is
Text Solution
Verified by ExpertsA
DR'S of OG=l, 1, 1
DR'S of AF = -l, 1, 1
DR'S of CE=l, 1,-1
DRS of BD =1,-1,1
Equation of OG 
Equation of AB 
Normal to both the line's
Ans.
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