For which $a∈R$ are the points P= (−1,2,1), Q= (−11,0,1), R= (a,−1,4) and S= (0,1,a) vertices in a tetrahedron?
Determine the area of the triangle PQR and the volume of the tetrahedron PQRS for such values of $a$. (Positively oriented ON-system assumed.)
I worked through it and found that in order for the 3 vectors that form the tetrahedron to be linearly independent, $a$ cannot be equal to 2. But how does this give us a fixed volume? I can only say that that the volume cannot be equal to $x$ given that a=2, but nothing more? I also know that the volume of a tetrahedron is 1/6 the volume of a parallelepiped made out of the same vectors, but dont know how this can help. Any help would be appreciated. Thank you!! :)