MathDB

Given is a trihedral angle

OABC

with a vertex

O

and a point

P

in its interior. Let

V

be the volume of a parallelepiped with two vertices at points

O

and

P

, whose three edges are contained in the rays

\overrightarrow{OA}

\overrightarrow{OB}

\overrightarrow{OC}

. Calculate the minimum volume of a tetrahedron whose three faces are contained in the faces of the trihedral angle

OABC

and the fourth face contains the point

P

Problem Statement