A course I'm doing has the following result quoted for two orthogonal vectors, $v$ and $w$ under a rotation in 3D space $v · w = Av · Aw$
= $(Av)^T*(Aw)$
= $v^T*(A^T*A)w$
= $v · (A^T*Aw)$
Now I can follow that until the last line since I believe $(AB)^T=B^T*A^T$, I don't understand the relation between the two last lines, how does $v^T$... become $v$ · ...?
Just expand quantities $v^Tw$ and $v\cdot w$ by coordinates and you'll see that $v^Tw=v\cdot w$.