The volume of the tetrahedron whose vertices are the points with positon vectors `hati-6hatj+10hatk, -hati-3hatj+7hatk, 5hati-hatj+hatk` and `7hati-4hatj+7hatk` is 11 cubic units if the value of `lamda` is

Options

A. `-1,7`
B. `1,7`
C. `-7`
D. `-1,-7`

Answer

B

Explanation

Let A,B, C and D be the points with the given position vectors. Then
`vec(AB)=-2hati+3hatj-3hatk, vec(AC)=4hati+5hatj+(lamda-10)hatk`
and `vec(AD)=6hati+2hatj-3hatk`
`:.` Volume `=11` cubic units.
`=1/6[(vec(AB), vec(AC), vec(AD))]=+-11`
`implies1/6|(-2, 3, -3),(4,5,lamda-10),(6,2,-3)|=+-11`
`implies-88+22lamda=+-66implieslamda=1` or `lamda=7`