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If V is the volume of the parallelopiped...

If V is the volume of the parallelopiped having three coterminus edges as a,b and c, then the volume of the parallelopiped having the edges as `alpha = (a.a)a+(a.b)b+(a.c)c; beta =(a.b)a+(b.b)b+(b.c)b;gamma=(a.c)a+(b.c)b+(c.c)c`, is

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