Tetrahedron & Parallelepiped in vector

Volume of tetrahedron and parallelepiped

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

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

Ratio Based Question|| Parallelepiped|| Vector Equation OF Line

If the verticles of a tetrahedron have the position vectors vec0, hati+hatj, 2hatj-hatk and hati+hatk then the volume of the tetrahedron is

Find the volume of a parallelepiped having three vectors of equal magnitude |vec a| and equal inclination theta with each other.

find the value of a so that th volume fo a so that the valume of the parallelepiped formed by vectors hati+ahatj+hatk,hatj+ahatkandahati+hatk becomes minimum.

Find the value of a so that the volume of the parallelepiped formed by vectors hat i+ahat j+k,hat j+ahat k and ahat i+hat k becomes minimum.

If the vertices of a tetrahedron have the position vectors vec 0,hat i+hat j,2hat j-hat k and hat i+hat k then the volume of the tetrahedrom is