Finding a perpendicular line that connects two skew 3D lines at a particular distance?

I have two linear, skew, 3D lines, and I was wondering how I could find a point on each of the lines whereby the distance between the two points are a particular distance apart, and that the vector formed between these points is perpendicular to both original lines?

I'm not after the points where the lines are the closest distance apart, nor the furthest distance apart! I'm after the points on the lines where the two lines are a particular distance apart and the vector between them is perpendicular. I'd like to also be able to change this distance and find the new points.

Please note that this is a different question to the one I posted here. I wanted to rewrite the question with the necessary changes because I got some really good answers to the last question I asked.

Thanks very much in advance for any help! :)

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If the vector between the points is perpendicular to both lines, then those points are the points where the distance is minimal. –  Hans Lundmark Mar 18 '11 at 11:18

1 Answer

You can't do this. If the lines are skew, there is only one line between them that is perpendicular to them both. (And if the lines are parallel, there are many such lines, but they all have the same length.)

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Whoops! Yea of course - I can see this now lol! –  James Bedford Mar 18 '11 at 13:21