Question

Show that the points P(-1,0,0), Q(2,-1,-1), R(0,3,1) and S(4,5,1) are vertices of a convex quadrilateral. A quadrilateral is convex if and only if none of its vertices is interior to the triangle determined by the other 3.

Answer 1

Not too sure what the fastest way of doing this is.
I guess you could define a plane that includes 3 of the points and then see the distance of the fourth point from that plane.
If it has a distance not zero (the likely outcome for randomly chosen points I would have said) you are done.

Answer 2

that works if the points aren't on the same plane, but they are coplanar... I sorta gave up on this one, thanks anyway :D