Hugh added the idea of justifying the changing four variables into two with ratios by saying "lets double the mass, lets triple the mass, quadruple . . . hey lets make this easy and not look at masses per say but ratios of masses and while we are doing that lets use the ratio of the distances."
The suggestion for talking the students to the vector nature is to look at the momentum before the explosion to see that it must be the same as after just like energy is conserved.