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

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];

 Respuesta aceptada

Matt J
Matt J el 9 de Abr. de 2021
Editada: Matt J el 9 de Abr. de 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

5 comentarios

And then I plug those values as a, b and c in ax+by+cz=d for each plane? But how do I get the value for d? Also, how do I proceed after that to get the equation of the straight line?
If I were to tell you all that, I would have done the whole problem for you.
Hussain Bukhari
Hussain Bukhari el 10 de Nov. de 2022
Editada: Hussain Bukhari el 10 de Nov. de 2022
Matt, what is this behavior?
@Hussain Bukhari - this is clearly a homework problem. And we try not to do homework assignments for students on Answers. Doing that does not help the student, beyond giving them an undeservedly good grade on their current homework. So @Matt J pointed the student in the right direction, but then stopped.
@John D'Errico, the response seemed quite abrupt so I was a little flummoxed.

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