A vector doesn't have a head and a tail. A vector in this context is something with a magnitude, and except for the zero vector, a direction. Another way to look at it: The displacement vector from the origin to the point with coordinates (1,1,1) and the displacement vector from the point with coordinates (2,2,2) to the point with coordinates(3,3,3) are the the same vector.
The angle between non-zero two vectors in three dimensional Euclidean space is determined by the ratio of the inner product between the vectors and the product of their magnitudes: $\cos\theta = (\mathbf a \cdot \mathbf b)/(||\mathbf a||\,||\mathbf b||)$. Once again, the head and tail don't come into play.
Does the centrifugal force change direction on an object moving along a circular path?
Imagine a kid on a playground roundabout. One moment the centrifugal force needed to keep her on the roundabout points south. A bit later, as the roundabout has made a quarter turn, the centrifugal force is pointing east. It's pointing north after yet another quarter of a turn, then west, then south again.
All that matters is the direction in which the force vector is pointing. If this direction changes over time, it's changing direction. It's as simple as that. You are overcomplicating things by asking about the head and tail of the vector.