Let A1A2A3A4 be a regular tetrahedron. Let P1 be the center of face A2A3A4 and define vertices P2,P3 and P4 the same way. Find the ratio of the volume of tetrahedron A1A2A3A4 to the volume of tetrahedron P1P2P3P4.
Using vectors, we can show that the ratio of the volume is 18.
That is incorrect.