How to find the gradient of a vector field and vector times the del operator?

Is there a way i can multiply a vector and the del operator, or gradient of a vector?


i know that gradient only can be used if it is a scalar?|||The del operator is a vector.








Gradient is like "scalar multiplication" of the del operator by a scalar function of space.








You can use vector multiplication of the del operator with a vector field, and there are two terms associated with doing so:





The divergence is like a "dot product" of the del operator with a vector field.


The curl is like a "cross product" of the del operator with a vector field.