$P_1$

$P_2$

$\vec{n_1}$

$\vec{n_2}$

P1: (3, 0, 6)
P2: (6, 1.5, 6)
E1: x + y + z = 9
E2: x + y + z = 13.5
X = PointIn(E2)
f = OrthogonalLine(X, E1)
A = Intersect(f, E1)
g = Segment(X, A)
n: (1, 1, 1)
Q1: P1 + n
Q2: P2 + (2 * n)
u = Vector(P1, Q1)
v = Vector(P2, Q2)