The unit tangent vector $\vec T (t)$ always has a magnitude of 1, though it is sometimes easy to doubt that is true. We can help solidify this thought in our minds by computing $\norm {\vec T (1)}$: ...

If the vertex shader output orientations (normal, tangent, light vector, half vector etc.) are not unit length then pixel shader interpolated inputs will be vastly off the supposed value, it will ...

In this problem, we know both the magnitude and direction for each of the velocity and acceleration vectors for the center of mass G. We know that the unit tangent vector e t is in the same direction ...