I am trying to use Mathematica to solve a very simple problem buy i don't manage to get the right answer.
The problem is to calculate the minimal area of a triangle where the 3 corners of the triangle is three coordinates in the 3d room. One of the coordinates have a variable "u"
The coordinates is
A = [8.32, 0, 4.583]
B = [0, 8.32, 4.583]
C = [8.32, 8.32, u + 4.583]
I have the following mathematic code to find the minimal area of the triangle but i don't get the right answer.
ClearAll["Global`*"]
a = {8.32, 0, 4.583}
b = {0, 8.32, 4.583}
c[u_] := {8.32, 8.32, (u^2) + 4.583}
ab = b - a
ac[k_] := c[k] - a
cr[n_] := Cross[ac[n], ab]
nr[p_] := Norm[cr[p]]/2
NMinimize[nr[p], p]
NMinimize[#.# &[Cross[{8.32, 8.32, u + 4.583} - {0, 8.32, 4.583}, {8.32, 0, 4.583} - {0, 8.32, 4.583}]], u]
give the expected result? $\endgroup$