inters α-β

inters α-γ

inters β-γ

$ \vec n_γ $

M*

B = -1 (slider from -5 to 5, step 0.1)
A = 2 (slider from -5 to 5, step 0.1)
D = 1 (slider from -5 to 5, step 0.1)
C = 1 (slider from -5 to 5, step 0.1)
A' = 1 (slider from -5 to 5, step 0.1)
B' = 3 (slider from -5 to 5, step 0.1)
C' = -1 (slider from -5 to 5, step 0.1)
D' = 1 (slider from -5 to 5, step 0.1)
β: (A' * x) + (B' * y) + (C' * z) + D' = 0
A'' = 3 (slider from -5 to 5, step 0.1)
B'' = 2 (slider from -5 to 5, step 0.1)
C'' = 0 (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
α: (A * x) + (B * y) + (C * z) + D = 0
a = IntersectPath(α, β)
b = IntersectPath(α, γ)
c = IntersectPath(β, γ)
n_α = OrthogonalVector(α)
n_β = OrthogonalVector(β)
n_γ = OrthogonalVector(γ)
A5 = 3
B5 = 2
C5 = 1
C6 = 23
A6 = 2
B6 = 1
M: {{A, B, C}, {A', B', C'}, {A'', B'', C''}}
M': {{A, B, C, D}, {A', B', C', D'}, {A'', B'', C'', D''}}
rangM = MatrixRank(M)
rangM' = MatrixRank(M')
P = Intersect(c, α)