There are many different electric toothbrushes, but I'm pretty sure that my Philips Sonicare operates on a single plane. The stem is like a pendulum. When brush is against my teeth it swings up and down (parallel to the teeth).
If it is powerful enough (and if the saw attached to it has fine enough teeth) it should work similarly to the Rockwell Sonicrafter (or similar) vibrating power tools.