Question

Find the Divergence of the vector field F at the given point.

vector field                                                   point

Answer 1

Step 1 :

If  is a vector field on  and  and  are exists, then the divergence of F is .

Step 2 :

The vector field is and the point is .

Compare with .

and .

Consider .

Apply partial derivative on each side with respect to x.

Consider .

Apply partial derivative on each side with respect to y.

Consider .

Apply partial derivative on each side with respect to z.

Step 3 :

Find the divergence of the vector field F.

Substitute corresponding values.

Substitute the point in above equation.

The divergence of the vector field F is

Solution :

The divergence of the vector field F is