Find the Value of the Constant $c$ Such That the Vector Field

Short Answer

Find the value of the constant $c$ such that the vector field
$$\mathbf { G } ( x , y , x ) = \left( 6 x + 2 y ^ { 3 } + 8 z \right) \mathbf { i } + \left( 6 x ^ { 3 } + 2 y + 4 z \right) \mathbf { j } + ( c z - x ) \mathbf { k }$$
is the curl of some vector field $\mathbf { F }$ .