# How to define for which plane lies a given point with coordinates?

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Aknur am 4 Apr. 2023
Hello!
Kindly ask about how to find in which plane lies point A(x, y, z), example A(1.5, 1.5, 3.0)
and I have planes
planes(:,:,1) = [0 3 3; 0 0 3; 0 3 0; 0 0 0];
planes(:,:,2) = [0 0 3; 3 0 3; 0 0 0; 3 0 0];
planes(:,:,3) = [3 0 3; 3 3 3; 3 0 0; 3 3 0];
planes(:,:,4) = [3 3 3; 0 3 3; 3 3 0; 0 3 0];
planes(:,:,5) = [0 3 0; 3 3 0; 0 0 0; 3 0 0];
planes(:,:,6) = [0 3 3; 3 3 3; 0 0 3; 3 0 3];
location_plane = 6;
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### Akzeptierte Antwort

Bjorn Gustavsson am 4 Apr. 2023
This is easiest to do with a vector-algebra approach. Something like this:
1, the plane can be described as all points such that , where is the normal to the plane and l is a scalar.
2, to use this, first use 3 of your 4 points to calculate the surface normal, (create 2 vectors that are not parallel, cross-multiply them and normalize that vector).
3, use the formula above with that normal-vector and all 4 points - to check that you get the same l for all four points.
4, test if also is identical to l
5, start over at point 1 with the next four points.
HTH
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Aknur am 6 Apr. 2023
I got same l for all 4 points (l0, l1, l2, l3 = =27), and l4 = dot(Pi,n) equal 0,
how then I can define on which plane lies my point with
Bjorn Gustavsson am 6 Apr. 2023
You have to make the same check with your point A. If you get the same l for as for one plane then A lies on that plane, if you get the same l for multiple planes then A lies in all those planes.

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