User:KohanX/Formulae

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The distance between two lines \mathbf{A} and \mathbf{B}, where \mathbf{a} and \mathbf{b} are the respective directions, and \mathbf{a^0} and \mathbf{b^0} are an arbitrary point along said lines, respectively. Both the directions and points are vectors, of course.

d(\mathbf{A},\mathbf{B})=\bigg|(\mathbf{a^0}-\mathbf{b^0})+\frac{((\mathbf{a}\cdot\mathbf{b})(\mathbf{b}\cdot(\mathbf{a^0}-\mathbf{b^0}))-(\mathbf{a}\cdot(\mathbf{a^0}-\mathbf{b^0})))\mathbf{a}-((\mathbf{b}\cdot(\mathbf{a^0}-\mathbf{b^0}))-(\mathbf{a}\cdot\mathbf{b})(\mathbf{a}\cdot(\mathbf{a^0}-\mathbf{b^0})))\mathbf{b}}{1-(\mathbf{a}\cdot\mathbf{b})^2}\bigg|