gistfile1.txt

to determine the intersection point of 3 planes in R^3:

if the 3 planes are specified using 4-component vectors a,b,c (a * v = 0 if the homogeneous vector v is on plane a, etc)

build the 4x4 matrix

(
x y z w
a^T
b^T
c^T
)

(x, y, z, w are helper symbols)

when you develop the determinant of the matrix along the x y z w row, the value of the subdeterminants (actually the cofactors, so including the (-1) powers) are the components of the generalized cross product result.

just divide by the w component to get the intersection point.