I've recently read about Null Identities of vector analysis. I'm having a problem in understanding what is it by "taking the curl of the grad of any scalar field is equal to zero." What is by definition of scalar field then? How would it looks like? Is position vector a scalar field? If No, then What's the difference between them? For say if i have a position field P, then by taking partial differentiation i achieve V (grad of P), which by means if i take the curl of V, does that means it is always irrotational no matter what? Thanks in advance.