Vector operator

A vector operator is a type of differential operator used in vector calculus. Vector operators are defined in terms of del, and include the gradient, divergence, and curl:

$\operatorname {grad} =\nabla$

$\operatorname {div} \ =\nabla \cdot$

$\operatorname {curl} =\nabla \times$

The Laplacian is

$\nabla ^{2}=\operatorname {div} \operatorname {grad} =\nabla \cdot \nabla$

Vector operators must always come right before the scalar field or vector field on which they operate, in order to produce a result:

$\nabla f$

yields the gradient of f, but

$f\nabla$

is just another vector operator, which is not operating on anything.