The physical and geometric interpretation of dr(t)/dt is the "velocity" of a point-like particle moving along the path r(t), treating r as the spatial position vector coordinates parametrized by time t, and is a vector tangent to the space curve for all t in the instantaneous direction of motion. At t = c, the space curve has a tangent vector , and the hyperplane normal to the space curve at t = c is also normal to the tangent at t = c. Any vector in this plane (p − a) must be normal to .
