Question: Let Q be the cube with the set of vertices {$(x_1, x_2, x_3) \in \mathbb{R}^3 : x_1, x_2, x_3 \in \{0, 1\}$}. 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 $l$ and $l'$, let $d(l, l')$ denote the shortest distance between them. Then the maximum value of $d(l, l')$ as $l$ varies over F and $l'$ varies over S, is
Options:
(a) $\frac{1}{\sqrt{6}}$
(b) $\frac{1}{\sqrt{3}}$
(c) $\frac{1}{\sqrt{5}}$
(d) $\frac{1}{\sqrt{2}}$
