How to find the normal vector on a Plane in 4d and above?

How to find the normal vector on a Plane in 4d and above?

If a plane in 4d contains the following points , how to find the normal vector on the plane?

P1 =[252716585.970010 -136769230.769231 0 0];

P2 =[ -136769230.769231 252716585.970010 -136769230.769231 0];

P3= [0 -136769230.769231 252716585.970010 -136769230.769231];

P4 = [0 0 -136769230.769231 126358292.985005];

Answer 1

[Torsten]

It's a vector orthogonal to P2-P1, P3-P1 and P4-P1 (which all lie in the plane), thus e.g.

P1 =[252716585.970010	-136769230.769231	0	0];
P2 =[ -136769230.769231	252716585.970010	-136769230.769231	0];
P3= [0	-136769230.769231	252716585.970010	-136769230.769231];
P4 = [0	0	-136769230.769231	126358292.985005];
n = null([P2-P1;P3-P1;P4-P1])

n = 4×1

0.2420 0.4472 0.5843 0.6325