Fig. P$3\mathrm{.}61$ and P$3\mathrm{.}62$

$3\mathrm{.}62$ A regular tetrahedron has six edges of length $a.($a$)$ Show that two opposite edges, such as $OA$ and $BC,$ are perpendicular to each other. $($b$)$ Use this property and the result obtained in Prob. $3\mathrm{.}61$ to determine the perpendicular distance between edges $OA$ and $BC.$