How to represent a 2D vector field in a way that will allow vectorial calculations (dot product)

Hello,

I'm trying to calculate the magnetic field created by a point dipole at an XY plane at some distance, the formula is as follows:

I have a 3x1 vector representing the magnetic dipole, and 3 N*N matrices for my grid: XGrid, YGrid, ZGrid.

The XY matrices were created using the meshgrid function and the ZGrid is a "constant" number that is the distance of the plane.

I can do something like: "r = cat(3, XGrid, YGrid, ZGrid)" and get a 60x60x3 array, but I am hoping for some method which will allow me to simply write afterwards "m.*r" or "m*r" and it'll return me a 60x60x3 array of the result.