The Force vector was expressed in terms of acceleration vector. Constant angular velocity was considered, and we found that the Force vector is parallel to the radial vector, indicating a centripetal force.
When a space curve is expressed in terms of a paramater t, which is interpreted as time, then the unit tangent vector points in the same direction as the velocity vector of a particle travelling on a path described by the space curve.
Acceleration can be expressed in terms of a tangential component and a centripetal (normal) component, the latter being proportional to the curvature of the path.
Newton's Law of Graitation was expressed in vector form. It is claimed that Kepler's First Law of Planetary Motion is a consequence of this. This will be proved next lecture. (You can also read about it in section 11.9 of the textbook.)