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how to find a point of 3 plane intersection

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Solve the system formed by the 3 plane equations , there are some detail about the theory , in particular about the determinat meaning that you may obtain imaginary intersections, just open a book about 3d geometry and read it.

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From three given plane equations:

ax + by + cz = j
dx + ey + fz = k
gx + hy + iz = l

You form a system:

AX = Y

where

a b c x j
A = d e f , X = y and Y = k
g h i z l

If det A is separated from 0 then the system has a uniqe solution.
Also, A is invertible and the solution can be written as follows:

X = inv(A)Y

where inv(A) means the inverse of A.
Here X holds the coordinates of the intersection point.


/Staffan

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