I've been investigating the shortest distance between two lines in terms of vectors. So far I have that you need to find the common perpendicular, from which I can get two equations with three unknowns. I believe it's possible to find the ratio of the unknowns from this, but I'm not sure how to go about it. Any help appreciated.
To put this into words, would this be the scalar product of (the line between a known point on each line) with (the unit vector for the scalar product of the direction vectors for each line)? I'm not sure of the significance of the 'x' signs.
Is there no merit in the other approach I mentioned?
I'm afraid so. I've finally got word back from the prof of my course and he says that we don't need to know it and haven't been taught it, even though it's on the official syllabus. I had wondered since, any way you cut it, it seems to involve mathematical techniques we haven't been taught yet.
Perhaps I'll investigate cross products anyway.
Thanks for the help.