The line L has equation:$$r=(i-4k)+t(i+2j-2k)$$ The line M has equation $$r=(4i+nj+5k)+s(7i+3j-4k)$$ where n is a constant.
Find (in terms of n) the shortest distance between lines L and M.
Here's what I've tried:
The direction vector of the line perpendicular to both L and M is $(2i+10j+11k)$.
So I tried to find the vector equation of the line perpendicular to both L and M then I can find the intersection of this line with L and M. (I failed to continue)
Then I tried to express the distance between the two lines in terms of $n$ and $t$
but I'm not sure whether the two 't' in the equation of L and M is the same..