Question

what is divergence and curl vector?

Answer 1

Curl of a Vector Field

The curl of a vector field F=<P(x,y,z),Q(x,y,z),R(x,y,z)>, denoted curlF, is the vector field defined by the cross product

An alternative notation is

The above formula for the curl is difficult to remember. An alternative formula for the curl is

det means the determinant of the 3x3 matrix. Recall that the determinant consists of a bunch of terms which are products of terms from each row. The product of the terms on the diagonal is

As you can see, this term is part of the x-component of the curl.

Consider the following example: F=<xyz,ysin z, ycos x>.

curl F = <cos x - ycos z, xy + ysin z, -xz>