Please show work

3. (a) Construct an example of two gradient fields F1(x,y) and F2(x, y) with the same field lines f(x,y) = C. Explain the method you used to construct this example and verify that the vectors Fi and F2 are perpendicular to the level sets f(x, y) = C. (b) Construct another example of two gradient fields with the same field lines either using the method outlined in part (a) or by coming up with another method. In the latter case, make sure to explain the second method used. Verify that the gradient field vectors are perpendicular to the field lines