2. Find the potential of the vector field F(x, y, 2) = exv/z ((14 2)it 2;2 zyg), and use the Fundamental Theorem for Line Integrals to evaluate F . dF , where C is the straight line segment from (1, 1, 1) to (2, 2, 1). Can one choose an arbitrary piece-wise smooth curve C with initial point (1, 1, 1) and terminal point (2, 2, 1) instead of the straight line segment? 6. Use the Fundamental Theorem for Line Integrals to find Jycos(ry) dr + (x cos(zy) - zev= )dy - yezdz, where C is the curve given by " ( t ) = (t, nt / 2, 1 - t), Osts1. 3. Consider the following vector field. F(x, y, z) = xi+ 1 + y 2 + 2 2 3 + 1 + 1 2 + 2 2 k . Z (a) Find curlF. (b) Is F conservative? Make sure to justify your claim. inbing lin