Question: How to show that these 2 procedures are correct or not?

A := [1, -2, 3]:u := `<,>`(0, -2, 2):v := `<,>`(5, 8, -3):
PL := proc (A, u, v) local d, Det, AP, t, U, V;
AP := `<,>`(x-A[1], y-A[2], z-A[3]);
Matrix(`<|>`(`<,>`(AP), `<,>`(u), `<,>`(v)));
Det := LinearAlgebra:-Determinant(%); d := igcd(coeff(Det, x), coeff(Det, y), coeff(Det, z), tcoeff(Det));
print(`Une équation cartésienne du plan est :`);
t := Det/d; print([t = 0]);
print('Une*représentation*paramétrique*du*plan*est; -1');
U := convert(u, list); V := convert(v, list);
[x = lambda*U[1]+mu*V[1]+A[1], y = lambda*U[2]+mu*V[2]+A[2], z = lambda*U[3]+mu*V[3]+A[3]] end proc;
PL(A, u, v);

plan3p := proc (A::list, B::list, C::list)
local d, M, N, P, Mat, Det, t, U, V;
M := `<,>`(x-A[1], B[1]-C[1], C[1]-A[1]); N := `<,>`(y-A[2], B[2]-C[2], C[2]-A[2]); P := `<,>`(z-A[3], B[3]-C[3], C[3]-A[3]);
Mat := Matrix([M, N, P]);
Det := LinearAlgebra:-Determinant(%);
d := igcd(coeff(Det, x), coeff(Det, y), coeff(Det, z), tcoeff(Det));
print(`Une équation cartésienne du plan est :`);
t := Det/d; print([t = 0]); print('Une*représentation*paramétrique*du*plan*est; -1');
U := A-B; V := B-C;
[x = lambda*U[1]+mu*V[1]+A[1], y = lambda*U[2]+mu*V[2]+A[2], z = lambda*U[3]+mu*V[3]+A[3]] end proc;
A := [-6, 3, -2]; B := [5, 2, 1]; C := [2, 5, 2];plan3p(A, B, C);
How to know if these procedures are correct or not. Thank you.