Prove that the shortest distance between any two opposite edges of a tetrahedron…

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Prove that the shortest distance between any two opposite edges of a tetrahedron formed by the planes y+z=0,x+z=0,x+y=0,x+y+z=3ay + z = 0, x + z = 0, x + y = 0, x + y + z = \sqrt{3}a is 2a\sqrt{2}a.

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