I know that neither of the two functions listed above are real, but I basically replaced vector for stream to give you an idea of what I want (the most ideal being a SliceStreamPlot3D as the StreamPlot3D would be pretty hard to visualize). Instead of seeing the magnitude of the vector at each location, I want to see the flow, i.e. a line with an arrow giving a direction (like the StreamPlot). I do not have a function to give you as the function I am using describes the magnetic field of a non ideal object and takes up three pages (it is an analytical solution; therefore composed of well defined functions).

Instead, say I have the function f{y,-x,z}, how can I show the StreamPlot say the x,y plane at z=0 and another StreamPlot on the y,z plane at x=0?