Potential of particle - why is there a scalar product here?

[tarkin2]

I'm reading up on the Lagrangian equation, but what I'm asking is to do with electromagnetism.

In the first equation here: http://www.phys.ufl.edu/~pjh/teaching/phy4605/notes/chargelagrangiannotes.pdf

L equals the kinetic minus the potential energy. For the potential energy term, I just don't see where the scalar product of magnetic potential and velocity is coming from. I haven't seen it written in this way before, could someone explain?

 

[Nguyen Son]

Hi Tarkin2, please move to part 4.4: Electromagnetism
https://en.wikipedia.org/wiki/Lagrangian_mechanics