Let F₁ and F₂ be the instantaneous forces that act on a particle with charge q when it moves through a magnetic field B(r) with velocities υ₁ and υ₂, respectively. Without choosing a coordinate system, show that B(r) can be determined from the observables υ₁ × F₁ and υ₂ × F₂ if υ1 and υ₂ are appropriately oriented.