Intersection of two planes ($n_1\times n_2$)

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.