inters α-β

$ \vec n_γ $

M*

inters γ-δ

C''' = -4 (slider from -5 to 5, step 0.1)
B''' = 0 (slider from -5 to 5, step 0.1)
A''' = -0.2 (slider from -5 to 5, step 0.1)
C'' = -3.2 (slider from -5 to 5, step 0.1)
B'' = 1.3 (slider from -5 to 5, step 0.1)
A'' = 3.8 (slider from -5 to 5, step 0.1)
D'' = -2.9 (slider from -5 to 5, step 0.1)
γ: (A'' * x) + (B'' * y) + (C'' * z) + D'' = 0
D''' = 4.1 (slider from -5 to 5, step 0.1)
δ: (A''' * x) + (B''' * y) + (C''' * z) + D''' = 0
D' = 4.1 (slider from -5 to 5, step 0.1)
D = -2.4 (slider from -5 to 5, step 0.1)
B = -4 (slider from -5 to 5, step 0.1)
A = 3.2 (slider from -5 to 5, step 0.1)
C = 3.4 (slider from -5 to 5, step 0.1)
A' = 0.5 (slider from -5 to 5, step 0.1)
B' = 2.6 (slider from -5 to 5, step 0.1)
C' = -1.4 (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)