Volume of tetrahedron and parallelepiped

Tetrahedron & Parallelepiped in vector

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of 27:1.

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of 27:1.

The volume of a tetrahedron fomed by the coterminus edges veca , vecb and vecc is 3 . Then the volume of the parallelepiped formed by the coterminus edges veca +vecb, vecb+vecc and vecc + veca is

The volume of a tetrahedron fomed by the coterminus edges veca , vecb and vecc is 3 . Then the volume of the parallelepiped formed by the coterminus edges veca +vecb, vecb+vecc and vecc + veca is

The volume of a tetrahedron fomed by the coterminus edges veca , vecb and vecc is 3 . Then the volume of the parallelepiped formed by the coterminus edges veca +vecb, vecb+vecc and vecc + veca is

Volume of parallelepiped determined by vectors bara,barb and barc is 5. Then the volume of the parallelepiped determined by the vectors 3(bara +barb). (barb + barc) and 2( barc + bara) is

Volume of parallelepiped determined by vectors bara,barb and barc is 5. Then the volume of the parallelepiped determined by the vectors 3(bara +barb). (barb + barc) and 2( barc + bara) is

Volume of parallelepiped determined by vectors vec a,vec b and vec c is 5. Then the volume of the parallelepiped determined by vectors 3(vec a+vec b),(vec b+vec c) and 2(vec c+vec a) is