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How to calculate the length of a vector at the point of intersection with a plane

Calculate the length of a vector, from the origin to the intersection with a plane.

We require:

a point P on the plane
the normal n of the plane
the intersecting vector v from the origin

We will now calculate d, which is the length of vector v needed for it to intersect the plane.

d =	( n_x × P_x ) + ( n_y × P_y ) + ( n_z × P_z )
	( n_x × v_x ) + ( n_y × v_y ) + ( n_z × v_z )

If the vector v was a unit vector (of length 1) then the length d is in units.

If the vector v was not a unit vector, then:

if 0<d<1 then the vector intersects the plane within its length
if d>1 then the vector intersects the plane after its length
if d<0 then the vector intersects the plane before the origin
if d=1 then the vector intersects the plane at the end of the vector

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