Intersection of two planes (source code)

= Intersection of two planes
{title2=$n_1\times n_2$}

Two <planes> $n_1\cdot r=d_1$, $n_2\cdot r=d_2$ with independent <normal vectors> meet in a <straight line> with direction $n_1\times n_2$. Any difference of two points on both <planes> is perpendicular to both <normal vectors>, which proves the direction statement. A particular point follows by solving the two <linear equations>; adding a real multiple of the direction gives the <parametric equation of a straight line>. For parallel <normal vectors>, the <planes> are either coincident or disjoint instead.