Letr=xi+yj+zkbe a displacement vector. We have:

$\displaystyle df=r.\nabla f$

Where f is a scalar field

What iffis a vector field. Does that mean that:

$\displaystyle df=r.\nabla f$

What about integration of scalar/vector fields with respect to vectors. I am interested in how you solve these:

$\displaystyle \int f \, dr$ Where f is a scalar field and

$\displaystyle \int g \, dr$ Where g is a vector field.

Any input is appreciated.