How to determine the directional behaviour of the magnetic vector potential?

I was wondering if someone could please help explain the directional behaviour of the magnetic vector potential? I understand that the magnetic vector potential $$A$$ is perpendicular to $$B=∇×A$$ but can someone please help explain why this is true?

The vector potential is defined by $${\bf B}=\nabla \times {\bf A}$$, but it is not uniquely defined. You can add the gradient of any scalar function to $${\bf A}$$ and $${\bf B}$$ will be unchanged.