Let C2 be the oriented curve parametriza r(t)= cost V2 ,sint, - cost V2 ), Osts2 n. Let F( x, y, z) = , and let I2=_ F-dr. [Suggestion: Use Stokes' Theorem and the fact that C 2 is the circle in the plane z = - X with radius 1 centered at the origin, (0,0,0).] 9. Let F(x,y.z) = . Evaluate JJ(V XF) .n do. Suggestion: Evaluate by calculating a surface integral over a surface in the XY-plane. Question 9 Compute (V X F) . ads for the vector field F given by F = xi+ (y + z + 4)j+ (2xyz8 + 6xz)k, where B is the part of the sphere x2 +y2 + 22 = 25 which lies below the plane z = -4, and n is the outward unit normal to the sphere. Question 1 Give an example of a non-constant vector field F which is defined in the whole plane and which has zero circulation along the following simple closed curve: x = 7% sin(t), y = 11 % cos(t), t E [0, 27]. Question 10 Let C be the intersection curve of the surfaces z = 3x - 7 and x2 + y = 1, oriented clockwise as seen from above. Let F = (42 - 1)i + 2x3 + (5y + 1)k. Compute the work integral F . dr = [ F . Tds two ways: (a) directly as a line integral (b) as a double integral, using Stokes' Theorem. 9. Let C be the curve of intersection of the cone x2 + y? = z and the plane z = 3. Let F(x,y,z) be the vector field yi + zj - x k . Let C be oriented clockwise as seen from above. Calculate F . dr (a) directly as a line integral AND (b) as a double integral, by using Stokes' Theorem