OABC is a tetrahedron. The position vectors of A, B and C are `i, i+j and j+k`, respectively. O is origin. The height of the tetrahedron (taking ABC as base) is

If the position vectors of the vertices A, B and C are 6i, 6j and k respectively w.r.t origin O, then the volume of the tetrahedron OABC is

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

If the position vectors of A,B,C and D are 2i+j,i-3j,3i+2j and i+lambda j respectively and bar(AB)||bar(CD) ,then lambda will be

OABC is a tetrahedron where O is the origin and A,B,C have position vectors veca,vecb,vecc respectively prove that circumcentre of tetrahedron OABC is (a^2(vecbxxvecc)+b^2(veccxxveca)+c^2(vecaxxvecb))/(2[veca vecb vecc])

The position vector of the points A, B and C are respectively vec i + vec j, vec j + vec k and lambda vec k + vec i . If the volume of the tetrahedron OABC is 6, find lambda where O is the origin.