Intersection of two lines

z=1

z

x

y

N1

Let homogeneous equations of the two lines be (N1,q)=0, and (N2,q)=0.

The two lines are intersections of planes with normals N1 and N2 with the plane z=1.

Intersection of lines = intersection point of the common line of the two planes with the plane z=1.

N2

The direction of

the common line

is the cross product:

This is also (one of possible) homogeneous forms of the intersection point!

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