Problem
When the $\mathbfit{\nabla}$ operator ($\mathbfit{\nabla}=\mathbfit{ \hat{x}}{\partial \over{\partial x}}+\mathbfit{ \hat{y}}{\partial \over{\partial y}}+\mathbfit{\hat{z}}{\partial \over{\partial z}}$) acts on a scalar function, the result is called the gradient.
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(a) What is the result called when $\mathbfit{\nabla}$ acts upon a vector function $\mathbfit F$ via the cross product: $\mathbfit{\nabla}\times \mathbfit{F}$? $$\\$$
(b) Using the determinant (matrix), derive the mathematical expression for $\mathbfit{\nabla}\times \mathbfit{F}$, if $F_x$, $F_y$, and $F_z$ are the projections of $\mathbfit F$ along the $x$, $y$, and $z$ axes, respectively. $$\\$$
(c) Is the result a vector or a scalar?