The solution method proposed by the editorial is non-obvious and possibly more complicated than it needs to be. A more intuitive and straightforward method (to this former vector calculus teacher) is to use parametric equations to describe the beampath and the wall. If Ri is the vector = , then problem can be rewritten " Does there exist an s and t (both between 0 and 1) so that s*R2 + (1-s)*R1 = t*Rm. From there it is straightforard linear algebra. The only special case that needs any particular care is the case where the lines are parallel, so the equations are indeterminate.