About perpendicularity of vectors

Question

If we have two perpendicular vectors $A$ and $B$ on the same surface and find another vector $C$ perpendicular to that surface such that $A \cdot C = 0$, then is true that $B \cdot C = 0$, too?

Answer 1

Clearly $B$ is perpendicular to $C$ so $B \cdot C = |B| |C| \cos \pi/2 = 0$.