Question

Determine whether or not the vector field is conservative. If it is comservative, find a function f such that F = Vf. (if the vector field is not conservative, enter DNE, . F(x,y,z)=15x²z²1+10x²yz³j+15x²y²z²k f(x,y,2)=

Answer 1

The vector field is not conservative and cannot be made conservative.

Step-by-step explanation:

To determine if a vector field is conservative, we need to check if the derivatives of its components satisfy a certain condition. If the derivative of the y-component of the force with respect to x is equal to the derivative of the x-component of the force with respect to y, then the force is conservative. In this case, since (dFx/dy) = 5 N/m and (dFy/dx) = 10 N/m, the force is not conservative.

To make this force conservative, you would need to change the derivatives to satisfy the condition mentioned earlier. Unfortunately, in this case, it is not possible to make the force conservative.