determining whether four pts are coplanar.?

Question

Here's the pts. Can you refresh me on how to do this. I need to kno if these 4 pts and coplanar--
P(1,0,1), Q(2,4,6), R(3,-1,2), S(6,2,8)

Answer 1

Take the determinant of the matrix:
|Px Py Pz 1|
|Qx Qy Qz 1|
|Rx Ry Rz 1|
|Sx Sy Sz 1|
in other words
|1 0 1 1|
|2 4 6 1|
|3 -1 2 1|
|6 2 8 1|

If the determinant is zero (it is), then the four points are coplanar.

Answer 2

Several ways to do it. I would get the vectors from P to Q and from P to R. Cross these to get the vector perpindicular to the plane of P, Q and R. Now dot this with a vector from any of P,Q, or R to S. This product must be zero if the 4 points are coplanar.