Vector Fields - Conservative Fields in Space

As it turns out, determining whether or not a vector field is conservative in space is radically different than that of a vector field in the plane. To determine whether or not a vector field is conservative in space (and by this, I mean 3D vector fields), we need to take the cross product of the gradient and our vector function. This yields a matrix:

This is called the curl of vector field F. If the curl is the zero vector, then the vector field is conservative.