inters α-β

$ \vec n_γ $

M*

inters γ-δ

$ \vec n_α $

$ \vec n_β $

C''' = 3 (slider from -5 to 5, step 0.1)
B''' = -2 (slider from -5 to 5, step 0.1)
A''' = 2 (slider from -5 to 5, step 0.1)
C'' = 2 (slider from -5 to 5, step 0.1)
B'' = 0 (slider from -5 to 5, step 0.1)
A'' = 3 (slider from -5 to 5, step 0.1)
D'' = 2 (slider from -5 to 5, step 0.1)
γ: (A'' * x) + (B'' * y) + (C'' * z) + D'' = 0
D''' = 2 (slider from -5 to 5, step 0.1)
δ: (A''' * x) + (B''' * y) + (C''' * z) + D''' = 0
D' = 0 (slider from -5 to 5, step 0.1)
D = 2 (slider from -5 to 5, step 0.1)
B = -2.2 (slider from -5 to 5, step 0.1)
A = 3.1 (slider from -5 to 5, step 0.1)
C = 1.4 (slider from -5 to 5, step 0.1)
A' = 1.5 (slider from -5 to 5, step 0.1)
B' = 2.1 (slider from -5 to 5, step 0.1)
C' = 4.3 (slider from -5 to 5, step 0.1)
β: (A' * x) + (B' * y) + (C' * z) + D' = 0
α: (A * x) + (B * y) + (C * z) + D = 0
r = IntersectPath(α, β)
n_α = OrthogonalVector(α)
n_β = OrthogonalVector(β)
n_γ = OrthogonalVector(γ)
M: {{A, B, C}, {A', B', C'}, {A'', B'', C''}, {A''', B''', C'''}}
rangM = MatrixRank(M)
M': {{A, B, C, D}, {A', B', C', D'}, {A'', B'', C'', D''}, {A''', B''', C''', D'''}}
rangM' = MatrixRank(M')
s = IntersectPath(γ, δ)
P = Intersect(r, s)
E = Point(r)
E' = Translate(E, n_α)
u = Vector(E, E')
E'_1 = Translate(E, n_β)
v = Vector(E, E'_1)
θ = Angle(u, v)