# Question:How do I write the equation of the plane passing through list of three points?

## Question:How do I write the equation of the plane passing through list of three points?

Maple

I have a code to write the equation of the plane passing through three points

restart:
with(geom3d):
point(A,1,-1,3):
point(B,-15,-17,11):
point(C,2,1,0):
plane(P,[A,B,C],[x,y,z]):
n:=NormalVector(P):
cdn:=ilcm(op(denom~(n))):
n:=cdn*n:
k:=igcd(n[1],n[2],n[3]):
if n[1]<>0 then sign(n[1])*cdn/k*sort(Equation(P))
elif n[2] <> 0 then sign(n[2])*cdn/k*sort(Equation(P))
else sign(n[3])*cdn/k*sort(Equation(P))
end;

How do I write the equation of the plane passing through list of following three points?
L := [[[-12, 2, -1], [-11, 1, -5], [-10, -2, 3]], [[-12, 2, -1], [-11, 1, -5], [-10, 6, 3]], [[-12, 2, -1], [-11, 1, -5], [-9, 5, -7]], [[-12, 2, -1], [-11, 1, -5], [-9, 8, -4]], [[-12, 2, -1], [-11, 1, -5], [-7, -6, -2]], [[-12, 2, -1], [-11, 1, -5], [-7, -2, -8]], [[-12, 2, -1], [-11, 1, -5], [-7, -2, 6]], [[-12, 2, -1], [-11, 1, -5], [-7, 3, -9]], [[-12, 2, -1], [-11, 1, -5], [-7, 3, 7]], [[-12, 2, -1], [-11, 1, -5], [-7, 6, -8]], [[-12, 2, -1], [-11, 1, -5], [-7, 9, 3]], [[-12, 2, -1], [-11, 1, -5], [-7, 10, -2]], [[-12, 2, -1], [-11, 1, -5], [-6, -4, -7]], [[-12, 2, -1], [-11, 1, -5], [-6, -4, 5]], [[-12, 2, -1], [-11, 1, -5], [-6, 8, -7]], [[-12, 2, -1], [-11, 1, -5], [-6, 8, 5]], [[-12, 2, -1], [-11, 1, -5], [-4, -6, 3]], [[-12, 2, -1], [-11, 1, -5], [-4, -2, -9]], [[-12, 2, -1], [-11, 1, -5], [-4, -2, 7]], [[-12, 2, -1], [-11, 1, -5], [-4, 6, -9]], [[-12, 2, -1], [-11, 1, -5], [-4, 6, 7]], [[-12, 2, -1], [-11, 1, -5], [-4, 10, 3]], [[-12, 2, -1], [-11, 1, -5], [-2, -6, 3]], [[-12, 2, -1], [-11, 1, -5], [-2, 6, -9]], [[-12, 2, -1], [-11, 1, -5], [-2, 6, 7]], [[-12, 2, -1], [-11, 1, -5], [-2, 10, 3]], [[-12, 2, -1], [-11, 1, -5], [3, 5, -7]], [[-12, 2, -1], [-11, 1, -5], [3, 8, -4]], [[-12, 2, -1], [-11, 1, -5], [4, -2, 3]], [[-12, 2, -1], [-11, 1, -5], [4, 6, 3]], [[-12, 2, -1], [-11, 1, -5], [5, 6, -2]], [[-12, 2, -1], [-11, 1, 3], [-10, -2, -5]], [[-12, 2, -1], [-11, 1, 3], [-10, 6, -5]], [[-12, 2, -1], [-11, 1, 3], [-9, 5, -7]], [[-12, 2, -1], [-11, 1, 3], [-9, 8, -4]], [[-12, 2, -1], [-11, 1, 3], [-7, -6, -2]], [[-12, 2, -1], [-11, 1, 3], [-7, -2, -8]], [[-12, 2, -1], [-11, 1, 3], [-7, -2, 6]], [[-12, 2, -1], [-11, 1, 3], [-7, 6, -8]], [[-12, 2, -1], [-11, 1, 3], [-7, 9, -5]]]

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