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

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Aknur
on 4 Apr 2023

Commented: Bjorn Gustavsson
on 6 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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### Accepted Answer

Bjorn Gustavsson
on 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

##### 12 Comments

Bjorn Gustavsson
on 6 Apr 2023

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