The postion vectors of the four angular points of a tetrahedron are `A(hatj+2hatk),B(3hati+hatk),C(4hati+3hatj+6hatk) and D(2hati+3hatj+2hatk)` find the volume of the tetrahedron ABCD.

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

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

Position vectors of four points A,B,C,D are 4hati +5hatj+hatk,-(hatj+hatk),3hati+9hatj+4hatk and 4(-hati+hatj+hatk) respectively . Prove that they are coplanar.

The volume (in cubic unit) of the tetrahedron with edges hati+hatj+hatk, hati-hatj+hatk and hati-2hatj-hatk is

The position vectors of the point A, B, C and D are 3hati-2hatj -hatk, 2hati+3hatj-4hatk, -hati+hatj+2hatk and 4hati+5hatj +lamda hatk , respectively. If the points A, B, C and D lie on a plane, find the value of lamda .

The position vectors of the point A, B, C and D are 3hati-2hatj -hatk, 2hati+3hatj-4hatk, -hati+hatj+2hatk and 4hati+5hatj +lamda hatk , respectively. If the points A, B, C and D lie on a plane, find the value of lamda .

Prove that the four points 6 hati - 7hatj, 16hati - 19 hatj - 4hatk, 3hatj - 6hatk and 2hati + 5hatj + 10 hatk form a tetrahedron in spacel.

Prove that the four points 6 hati - 7hatj, 16hati - 19 hatj - 4hatk, 3hatj - 6hatk and 2hati + 5hatj + 10 hatk form a tetrahedron in spacel.

The volume (in cubic unit ) of the tetrahedron with edges hati+hatj+hatk, hati-hatj+hatk and hati+2hatj-hatk , is