1.
AB = [-5, 1, 0]
AC = [-4, 0, 2]
n = [-5, 1, 0] ⨯ [-4, 0, 2] = [2, 10, 4] = 2·[1, 5, 2]
E: (X - [3, 1, 1])·[1, 5, 2] = 0
E: x + 5·y + 2·z = 10
g3 in E einsetzen
(5 + k) + 5·(- 12 + 5·k) + 2·(-5 + 2·k) = 10 → k = 2.5
S = [5, -12, -5] + 2.5·[1, 5, 2] = [7.5, 0.5, 0]