= Line-plane incidence in Plücker coordinates
{title2=$P^i=L^{ij}F_j,\quad F_i=L_{ij}D^j$}
The intersection of a line in <Plücker coordinates> with a plane covector $F$ is the first displayed homogeneous vector: it lies in the span of the defining points and its contraction with $F$ is zero by antisymmetry. A zero vector means the whole line is contained in the plane. Dually, the plane through the line and a point or ideal direction $D$ is given by the second formula; it vanishes if $D$ is already on the line. These operations require no Euclidean lengths or angles.
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