Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the vector field is not conservative, enter dne.) f(x, y, z) = 7y2z3 i + 14xyz3 j + 21xy2z2 k

Solution:

Given: F(x, y, z) = 7y²z³ i + 14xyz³ j + 21xy²z² k

F is a conservative field if curl F = 0, there exist a scalar potential function  such that F = .

curl f =

Thus,curl F is conservative.

To find f such that F = gradf.

Integrate the above terms with respect to x.

Hence, the scalar potential function is .

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column

30005

yes ok