# How do I find the line representing the intersection of two planes?

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Felipe Dicker on 9 Apr 2021
Commented: Matt J on 9 Apr 2021
So basically I have two planes and need to find the equation of the straight line which is the intersection between the two. I'm having trouble finding the equation of said planes and then equaling them to each other to find the equation of the straight line. I do know the coordinates of three points on each one of the planes. Any help? Here are the points:
% Plane 1
A = [1 1 1];
B = [2 -3 5];
C = [-7 2 1];
% Plane 2
D = [0 5 3];
E = [8 -4 2];
F = [5 4 1];

Matt J on 9 Apr 2021
Edited: Matt J on 9 Apr 2021
HINT: You can get the normals to the planes using cross()
% Plane 1
A = [1 1 1];
B = [2 -3 5];
C = [-7 2 1];
% Plane 2
D = [0 5 3];
E = [8 -4 2];
F = [5 4 1];
normal1=cross(B-A,C-A)
normal1 = 1×3
-4 -32 -31
normal2=cross(E-D,F-D)
normal2 = 1×3
17 11 37
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Matt J on 9 Apr 2021
If I were to tell you all that, I would have done the whole problem for you.