Let F(x, y, z) = (x-1z, y¬lz, In(xy). (a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy). (b) Evaluate F. dr, where r(t) = (e', e²" , r²) for 1 < 1 < 3. . (c) Evaluate F. dr for any path C from P = (}, 4, 2) to Q = (2, 2, 3) contained in the region x > 0, y > 0. (d) Why is it necessary to specify that the path lies in the region where x and y are positive?

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