




A vector field is a vector each of whose components is a scalar field, that is, a function of our variables. We use any of the following notations for one:
v(x, y, z) = (v_{1}(x, y, z), v_{2}(x, y, z), v_{3}(x, y, z))
v(x, y, z) = v_{1}(x, y, z)i + v_{2}(x, y, z)j + v_{3}(x, y, z)k
v(x, y, z) = (L(x, y, z), M(x, y, z), N(x, y, z))
One important class of vector fields are those that are gradients of a scalar field. If f is a scalar field, its gradient,f, is a vector field, namely