Mathematically a vector in the plane is just an ordered pair of real numbers. Physicists tend to embellish this rather spare definition so that their vectors are represented by arrows with direction and magnitude indicating the direction and strength of forces, velocities, and accelerations among other things. Consider a point moving in the xy coordinate plane so that it traces out some curve as the path of its motion. As the point moves along this curve, the x and y coordinates are changing as functions of time. Suppose that x=f(t) and y=g(t). Now the mathematician will say that the position at any time t is (f(t),g(t)) and will say that the position vector for the point is R(t)=(f(t),g(t)). The physicist will say that the position vector R(t) is an...