Originally Posted by

**Mush** $\displaystyle \nabla f $ is the gradient of scalar field f. A vector does not have a gradient in this sense. A vector can have curl and divergence, but not gradient. The gradient of a scalar field is a vector field.

Nabla, is defined as : $\displaystyle \nabla = (\frac{d}{dx},\frac{d}{dy},\frac{d}{dz}) $

If you have a vector $\displaystyle \vec{f}=(F_x,F_y,F_z)$, then you can have only two multiplicative operations with this vector and the nabla vector. Those are the dot product ($\displaystyle \nabla . \vec{f} $)and the cross product ($\displaystyle \nabla \times \vec{f} $). And these represent divergence and curl respectively. It does not make sense to have scalar multiplcation between two vectors, which is what you are proposing with $\displaystyle \nabla \vec{f}$.

You may have scalar multiplication between two scalars, and scalar multiplcation between a scalar and a vector (a lá, $\displaystyle \vec{grad}(f)$, but you may not have scalar multiplication between two vectors.