Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. 5) F = 2yi + 3xj + 623k ; C: the portion of the plane 3x + 3y + 5z = 6 in the first quadrant 5) A) 0 B) - 2 C) 1 D) 2 6) F = 3yi + yj + zk; C: the counterclockwise path around the boundary of the ellipse X2 yz 9 25 - = 1 6) A) 457 B) 157 C) -45n D) -45Using the Divergence Theorem, find the outward flux of F across the boundary at the region D. 1"] F = zi + xyj + zyk: D: the solid cube cut by the coordinate planes and the planes 3: = 2.1-; = 2. and z = T} 2 A) 2 B] 16 C} 4 D} 32 8) F = x21+ yzj + 2k: D: the solid cube cut by the coordinate planes and the planes 3: = 3, y = 3. and z = 3] 3 A3108 B] 1154 C181 [3139 Find the flux of the curl of field F through the shell S. 9) F = exi + eyj + 3xyk; S is the portion of the paraboloid 2 - x2 - yz = z that lies above the xy-plane 9) A) 48 B) - 48 C) 0 D) -48n 10) F= -5x2yi + 5xy2j + z2k: $ is the portion of the paraboloid 2 - x2 - y? = z that lies above the 10) xy-plane A) 80 40 B) 3 C) 10rt D) 80m