# Proving the direction of a parallel transported vector (Riemann and Psueudo Riemann) changes

As the title suggests, I am trying to find a method of proving that the direction of a parallel transported vector changes direction for Riemann or Pseudo Riemann manifolds.

I can easily show that the length of vector doesnt change when parallel transported by just showing:

$$\frac{dv^2}{du}=0$$ With $$v^2=v^av_a\$$ and u= Affine parameter

I am not sure how to show though that the direction does change, and get stumped when directions are involved. This question is for studying and not homework.