A vector operator is a differential operator used in vector calculus.
Vector operators include: Defined in terms of del: The Laplacian operates on a scalar field, producing a scalar field: Vector operators must always come right before the scalar field or vector field on which they operate, in order to produce a result.
E.g. yields the gradient of f, but is just another vector operator, which is not operating on anything.
A vector operator can operate on another vector operator, to produce a compound vector operator, as seen above in the case of the Laplacian.