= Joint of a line collection
{title2=$x\in\ell_1\cap\cdots\cap\ell_n,\quad\operatorname{span}(v_1,\ldots,v_n)=\mathbb R^n$}
= Joint
{synonym}
= Joints of a line collection
{synonym}
For distinct real affine lines in $\mathbb R^n$, $n\ge2$, a <joint of a line collection> is a point lying on $n$ lines with <linearly independent> direction vectors. In three dimensions the directions must not all lie in one plane. Extra incident lines are allowed; existence of one spanning choice is enough. This counts <joint of a line collection> points, rather than tuples of lines or incidence multiplicities.
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