Jelly, 5 bytes Takes input in the form \$[[x_1,x_2],[y_1,y_2],[z_1,z_2]]\$. If you want them to be two lists of x-y-z coordinates, just prepend Z to the beginning of the program. ṁ4ÆḊƝ Try it online! Here is an explanation of how this works. I'll migrate it to SE markdown shortly.