Prove that the shortest distance between the diagonals of a rectangular parallelepiped whose coterminous sides are a, b, c and the edges not meeting it are 
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Let coordinates of rectangular parallelepiped are A(0,0,0); B(a,0,0); C(a,b,0); D(0,b,0); E(0,0,c); F(a,0,c); G(a,b,c); H(0,b,c). Then equation of diagonal AG is 
and equation of BC is 
⇒ shortest distance between AG and BC = 
= 
Similarly shortest distance between AG and DC = 
Similarly shortest distance between AG and BF = 
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