6. [-/1 Points] DETAILS SCALC9 16.8.012. Use Stokes' theorem to evaluate / F . dr. F(x, y, z) = ze*1 + (2 - 3y )j + (x - 323) k, Cis the circle y? + 27 = 16, x = 5, oriented clockwise as viewed from the origin Need Help? Read It Submit Answer 7. [1/8 Points] DETAILS PREVIOUS ANSWERS SCALC9 16.8.017. Verify that Stokes' theorem is true for the given vector field F and surface S. F(x, y, z) = -yl + xj - 2k, S is the cone z? = x2 + y?, 0 s z s 3, oriented downward The boundary curve C is the circle x2 + y2 = 9 with z = 3 as viewed from above is oriented in the clockwise direction. We can parametrizat (cos(t) 1 - sin(t)j + k), 0 s t s 2x, and then r'(t) =( (-sin(t) 1 - cos(t)j). Thus, F(r(t)) = since) + ( cos(t)j - 2k and we find that F(r(t)) . r'(t) = , and { F . de = ("F(r(E)) . r'(t) at = Now curl(F) = 2k, and the projection D of S on the xy-plane is the disk x2 + yz s 9, so by the equation 1/ F . as = 1/ ( -P- - 92+ R) dA with z = g(x, y) = v x2 + y? [by multiplying by -1 for the downward orientation] we have CURCE) . as = - /6 (-0- 0+2) dA = Need Help? Read It Watch it Submit Answer 8. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 16.8.021. A particle moves along line segments from the origin to the points (3, 0, 0), (3, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field F(x, y, z) = 221 + 3xyj + 5yzk. Find the work done. F . dr = 388.125 x Need Help? Read It Watch it Submit