Final answer:
The tangential acceleration vector is linear and parallel to the tangential velocity. The centripetal acceleration points inward toward the center of the circle. Both accelerations are important for objects moving in an elliptical path.
Step-by-step explanation:
In the context of an elliptical path, the tangential acceleration vector is the acceleration in the direction tangent to the circle at the point of interest. It is a linear acceleration that is parallel to the tangential velocity. On the other hand, the centripetal acceleration vector is the acceleration in the radial direction, pointing inward toward the center of the circle. It is responsible for changing the direction of the tangential velocity and keeping the object on the elliptical path.