$\vec{n}$

B1: (4, 0, 0)
C1: (4, 4, 0)
S: (2, 2, 8)
p = Plane(B1, C1, S)
P: (3, 2, 4)
n: (4, 0, 1)
u: (0, 4, 0)
v: (-1, 0, 4)
A: P + u + v
B: P - u + v
C: P - u - v
D: P + u - v
N: P + n
w = Vector(P, N)
v1, a, b, c, d = Polygon(A, B, C, D)
U: P + u
V: P + v