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.

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 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

The volume of a tetrahedron formed by the coterminous edges vec a,vec b, and vec c is 3. Then the volume of the parallelepiped formed by the coterminous edges vec a+vec b,vec b+vec c and vec c+vec a is 6 b.18 c.36 d.9

If the volume of the parallelepiped formed by the vectors veca xx vecb, vecb xx vecc and vecc xx veca is 36 cubic units, then the volume (in cubic units) of the tetrahedron formed by the vectors veca+vecb, vecb+vecc and vecc + veca is equal to

The volume of a tetrahedron determined by the vectors veca, vecb, vecc is (3)/(4) cubic units. The volume (in cubic units) of a tetrahedron determined by the vectors 3(veca xx vecb), 4(vecbxxc) and 5(vecc xx veca) will be

If V be the volume of a tetrahedron and V' be the volume of another tetrahedran formed by the centroids of faces of the previous tetrahedron and V=KV', then K is equal to 9 b.12 c.27 d.81

If the vectors 2hat i-3hat j,hat i+hat j-widehat k and 3hat i-hat k form three concurrent edges of a parallelepiped,then find the volume of the parallelepiped.