Magnitude of dipole moment is basically charge times distance, right? So if the center of the molecule is placed at the cartesian origin, then the sum of all the vectors (charge times displacement) must be zero for a molecule with zero dipole moment. To make things easy, then, you can separate this into three problems, one for each unit direction (x,y,z). So, for the z-direction you need to show that the charge times distance for each atom along the z direction equals zero. Here you have things easy because each chlorine has the same charge, which we can assign as "1". Therefore you just need to show that Σ*d*_{zi} = 0, where *d*_{zi} is the displacement of the *i*th chlorine along the z axis. For example, *d*_{zi} for the chlorine just above the carbon center (along the z-axis, in the system I described in the previous post), would be exactly 1. So you need to find the analogous values for the other three chlorines, and show that they equal -1 in total, so that the overall total z-displacement of charge is equal to zero. Then do the same for x and y.

(The z direction is fairly easy. The x and y direction requires some more complicated geometry and trigonometry, but still the approach is generally the same.)