9. [-/2 Points] DETAILS LARCALCET7 15.8.003. MY NOTES ASK YOUR TEACHER Verify Stokes's Theorem by evaluating F . dr as a line integral and as a double integral. F ( x, y, z) = ( -y + z)i + (x - z)j + (x - y)k S: z = 16 - x2 - y2, z20 line integral double integral 10. [-/1 Points] DETAILS LARCALCET7 15.8.007. MY NOTES ASK YOUR TEACHER Use Stokes's Theorem to evaluate F . dr. In this case, C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + 3zj + xk C: triangle with vertices (4, 0, 0), (0, 4, 0), (0, 0, 4) 11. [-/1 Points] DETAILS LARCALCET7 15.8.015. MY NOTES ASK YOUR TEACHER Use Stokes's Theorem to evaluate F . dr. In this case, C is oriented counterclockwise as viewed from above. F ( x, y, z) = xyzi + yj + zk S: z = x2, Osxsa, Osysa N is the downward unit normal to the surface. 12. [-/5 Points] DETAILS LARCALCET7 15.8.017. MY NOTES ASK YOUR TEACHER The motion of a liquid in a cylindrical container of radius 2 is described by the velocity field F(x, y, z). Find / / (curl F) . N as, where S is the upper surface of the cylindrical container. F (x, y, z) = - -y3i + _x3j+ 7k