- 3 Consider The Vector Field Y X F J Zk X Y X Y A Let C Be The Curve In The Xy Plane Given By X Y 1 (141.82 KiB) Viewed 30 times
3. Consider the vector field -Y X F = j + zk x² + y² x² + y²° (a) Let C be the curve in the xy-plane given by x² + y² = 1 oriented counter clockwise when viewed from above. Calculate the line integral SF. dr. (b) Now, find the curl of the vector field. (c) Let S be the part of the sphere x² + y² + z² = 1, z 20. What is wrong with the following statement? From part b, we can use Stokes' theorem to conclude the following: curl F. ds = If cur ffo.as dS = F. dr = 0 S S 1 4. Let u u₁i+u₂j + u3k be a constant vector. Let r= xi + yj + zk. (a) Calculate rx u. (b) Find the divergence of the vector field found in part (a). (c) Calculate the flux of the vector field found in part (a) out of a cube with sides equal to 4 units centered at the origin with edges parallel to the coordinate axes. The cube is oriented outwards. i+