# Thread: Shortest Distance between lines (3D) NEED HELP

1. ## Shortest Distance between lines (3D) NEED HELP

Hi Everyone, I have this question I try to solve it with the formula but it does not work.
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Find the shortest distance between the line r = Xi+Yj+Zk = i + j - k +sU and r= tV and UxV is not equal to zero

2. ## Re: Shortest Distance between lines (3D) NEED HELP

Originally Posted by angelme
Find the shortest distance between the line r = Xi+Yj+Zk = i + j - k +sU and r= tV and UxV is not equal to zero
I feel sorry for you. Whoever wrote you text/notes does not use standard notation nor symbols.
I can give you the standard answer.
If each of $\ell_1:P + tU\;\& \;{\ell _2}:Q + tV$ and $U\times V\ne 0$ the distance between them is
$\frac{{\left| {\overrightarrow {PQ} \cdot \left( {U \times V} \right)} \right|}}{{\left\| {U \times V} \right\|}}$

I hope you can use this in some way.