What is ohm's law in vector form?

 

A vector has 3 propriety, direction in space, versus and the algebric value. On the other hand a scalar is just a number. Electric current is a scalar despite the fact the current have a numerical value and a precise versus in space, but dont have a specific direction in space, the direction of the electric current follow the direction of the wire, so the Current is a scalar, like the voltage.

 

However, as you have asked what is the vector 'form' of the Ohm's Law, it is,

 

 

j=σE,

   

Where j the current density SI unit : A/m²

E is electric field with SI unit V/m

σ is the conductivity (reciprocal of resistivity).