I know there must be an elegant solution I’m just not thinking of here:

Given: two points A and B and a line C,

I’m looking to find: the point X on line C, where line AXB has the minimum distance of any possible point on C.

I realize that if line C is co-planar with A and B, then X can be thought of as the tangent point of an ellipse tangent to C and with foci A and B.

If line C is NOT co-planar with A and B, then X can be thought of as the tangent point of an *ellipsoid* tangent to C and with foci A and B. Not sure if this helps us at all…

I know there must be an elegant algebraic solution here I’m just not seeing… Anyone have any ideas?

Thanks!

WD