Grad, curl , div operator got any meaning?

[Outrageous]

grad, curl , div operator got any meaning??

∇x F (t) same as the first derivative of F with respect to t , or will get the gradient of F which is normal to the F ?
∇ dot F (t) , will get the scalar value of what??
lets say F is force , then can anyone please give me the meaning of those operator on the vector mean?
∇x F (t) will get the gradient of F which is normal to the F .
I think of this because in the stoke's theorem the ∇x F (t) have to dot with n , where n should be the unit normal vector of the surface.
I am blur , please guide .
Thank you.

 

[Integral]

First check the definition of Del as given in wiki.

Note that it is defined as the differential with respect to spatial coordinates, not time.

 

[MisterX]

Your use of the word "normal" is not correct. F is a vector field, not a surface. Perhaps you meant orthogonal instead of "normal".

∇x F is not the "the gradient of F which is normal to the F".