Let F(-2y, 4.x2, 1422). Evaluate F. dr Where C is the intersection of the plane 2x...
Let F = ( – 4y, 1x2, 322). Evaluate so . dr Where C is the intersection of the plane 9x + 4y +z = 2 and the cylinder a2 + y2 = 9, positively oriented as seen from above. Assume the conditions of Stoke's Theorm have been met. answer = 7
Use Stokes' Theorem to evaluate / F. dr, where F = -7y’i + 7x'j + 2zk and C is the intersection of the cylinder x2 + y2 = 1 and the plane 1x + 4y + z = 9 (oriented counterclockwise as seen from above). [F.dr =
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of the plane x z 8 and the cylinder x2 y9oriented counterclockwise as viewed from above. Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented upwards curl(2xyi+zj +3yk)- 2,0,-2x The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z-8. Using this surface in...
Use Stoke's Theorem to evaluate ScF. dr, where F(x, y, z) = -xzzi + y2zj + zºk and C is the curve of intersection of the planez = 1 – X – Y and the cylinder x2 + y2 = 1, oriented counterclockwise as viewed from above.
Use Stokes' Theorem to evaluate ∫??⋅??∫CF⋅dr, where ?=−3?3?+3?3?+9?3?F=−3y3i+3x3j+9z3k and ?C is the intersection of the cylinder ?2+?2=1x2+y2=1 and the plane 3?+4?+?=63x+4y+z=6 (oriented counterclockwise as seen from above). ∫??⋅??=∫CF⋅dr=
please show all work Use Stokes' Theorem to evaluate Sc F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyl +22+ 4yk, C is the curve of intersection of the plane X + 2 = 10 and the cylinder x2 + y2 - 36.
5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 and the surface:-10 + 0.4xy, and F = 《2xz-2y, 2y2+ 2x, x2 + y2 + z?) is a given vector field. Find the circulation F dr 5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 and the surface:-10 + 0.4xy, and F = 《2xz-2y, 2y2+ 2x, x2 + y2 + z?)...
3] (a) Use Stoke's Theorem to evaluate ScF. dr by evaluating the related double inte- gral, where F(x, y, z) = (x2z, cy, 22) and C is the curve of intersection between the plane x+y+z=1 and the cylinder ? + y2 = 9 oriented clockwise when viewed from above. (b) Sketch a graph of both the plane and cylinder with so that the intersecting curve is clear. 2) Find the parametric equations for C and use them to sketch a...
Let F(x, y, z) be the gradient vector field of f(x, y, z) = exyz , let C be the curve of the intersection of the plane y + z = 2 and the cylinder x2 + y2 = 1, oriented counterclockwise, evaluate Sc F. dr. OT O -TT O None of the above. 00
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...