A = [3, 4, 1]
B = [0, 1, -1]
C = [-2, 3, 0]
Richtungsvektoren der Seiten
AB = [-3, -3, -2]
AC = [-5, -1, -1]
BC = [-2, 2, 1]
Höhenfußpunkt
FAB = [3, 4, 1] + [-3, -3, -2]·[-5, -1, -1]/([-3, -3, -2]·[-3, -3, -2])·[-3, -3, -2] = [3/11, 14/11, -9/11]
FAC = [3, 4, 1] + [-3, -3, -2]·[-5, -1, -1]/([-5, -1, -1]·[-5, -1, -1])·[-5, -1, -1] = [-19/27, 88/27, 7/27]
Schnittpunkt der Höhen
[-2, 3, 0] + r·([3/11, 14/11, - 9/11] - [-2, 3, 0]) = [0, 1, -1] + s·([- 19/27, 88/27, 7/27] - [0, 1, -1]) --> r = 77/97 ∧ s = 27/97
S = [-2, 3, 0] + 77/97·([3/11, 14/11, - 9/11] - [-2, 3, 0]) = [-19/97, 158/97, -63/97] = [-0.1959, 1.6289, -0.6495]