1. The problem statement, all variables and given/known data [PLAIN]http://img835.imageshack.us/img835/1108/question.png [Broken] 3. The attempt at a solution I understand that the determinant represents the set of points, x in R_k which lies in the hyper plane passing through the points p1, p2.....p_k. I also know, that if the determinant is non zero, and the sign is opposite for two choice of x, then they must be on different side of the hyper plane. However, i am not too sure how can i prove this. My first thought is that this looks like the determinant to a Jacobian, but can't proceed much beyond that. Any hints and helps is appreciated. Thanks.