The volume of the tetrahedron whose vertices are the points with position vectors $\hat i-6\hat j+10\hat k, -\hat i-3\hat j+7\hat k, 5\hat i-\hat j+2\hat k$ and $7\hat i-4\hat j+7\hat k$ is 11 cubic units if the value of $λ$ is

-1, -7

Let A, B, C and D be the points with the given

$\vec{AB}=-2\hat i +3\hat j-3\hat k, \vec{AC} =4\hat i +5\hat j+(λ-10)\hat k$ and, $\vec{AD}=6\hat i +2\hat j-3\hat k$.

∴ Volume = 11 cubic units

$⇒\frac{1}{6}[\vec{AB}\,\,\vec{AC}\,\,\vec{AD}]=±11$

$⇒\frac{1}{6}\begin{vmatrix}-2&3&-3\\4&5&λ-10\\6&2&-3\end{vmatrix}=±11$

$⇒-88+22λ=±66⇒λ=1$ or $λ=1$