2). Use Stokes' theorem to evaluate the integral 6 F • dř for F(x, y, z) = (x – y)î + (y – z)ĵ + (z – x)k and C is the circle x² + y² = a° in the xy plane with counterclockwise orientation looking down the positive z axis.

Use Stokes's Theorem to show that 0 = || curl(F) - dS where F(r, Y, z) = (2, 2xy, x + y) and S is the surface of a glass oriented outwards whose open cap is a circle with equation r? + (z – 2)2 = 9. Hint: For the circle you can e the parametrixation r(t) = (3 can t, 0, 3 xin t + 2), te [o, 27]

Use Stokes' Theorem to evaluate F(x, y, z) = (x + y²)i + (y + z²)j + (z + x²)k, C is the triangle with vertices (5, 0, 0), (0, 5, 0), and (0, 0, 5). Enter an exact number. I F. dr where C is oriented counterclockwise as viewed from above. Submit Answer