Free particles move with constant velocity.
The vector force is proportional to the rate of change of momentum i.e. . To every action there is an equal and opposite reaction. Here is a rotation matrix aligning and , is the relative velocity of with respect to and is the displacement of the origin from . Thus there are an infinite set of inertial frames, all moving uniformly with respect to each other. All of Newtons laws apply in any inertial frame since and is invariant.