The tetrahedron defined by three vectors 5i, 52,53 in R3 is the set of all vectors of the form c\v\ + C2V2 + C3U 3, where c,- > 0 and c\ + C2 + C3 < 1. Explain why the volume of this tetrahedron is one-sixth of the volume of the parallelepiped defined by 5j, 52, 53.

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