Über Formel
F = A + (AC·AB) / (AB·AB)·AB
= [1, 1, 2] + [2, 3, 2]·[4, 1, 1] / ([4, 1, 1]·[4, 1, 1])·[4, 1, 1] = [35/9, 31/18, 49/18]
Über Orthogonalitätsbedingung
AB = B - A = [5, 2, 3] - [1, 1, 2] = [4, 1, 1]
F = A + r·AB = [1, 1, 2] + r·[4, 1, 1] = [4·r + 1, r + 1, r + 2]
CF = F - C = [4·r + 1, r + 1, r + 2] - [3, 4, 4] = [4·r - 2, r - 3, r - 2]
AB·CF = [4, 1, 1]·[4·r - 2, r - 3, r - 2] = 18·r - 13 = 0 → r = 13/18
F = A + r·AB = [1, 1, 2] + 13/18·[4, 1, 1] = [35/9, 31/18, 49/18]