:) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with vertices (2,0,0), (0,2,0) and (0,0,2) with BUTM EUTM anticlockwise direction when viewed from above. TM UTM

Q: (5) Evaluate F- dr using Stokes' Theorem, where F(1, y, 2) = -y?i + xj +2²k and C is the curve of…

A:

Q: O) Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xyi + j + xyk and C is the curve of…

A: (c) The curve, C can be easily parametrized using the following parametrization: x=cos t, y=sin t…

Q: Consider the surface S: z = 4ex^2  - 4xy, where P (0, 1, 1) is a point on S. An equation of the…

A: A detailed solution is given below.

Q: Let y be the boundary of the parallelogram formed by the = (1, –1,0), C = (2,0, 2) and D = (1, 1, 2)…

A: The curl of the vector field curlF→=i→j→k→∂∂x∂∂y∂∂z2xz-2yz+x+sin(y2)2z+x2+2y curlF→=i→+3k→

Q: Use Stokes' Theorem to evaluate ſc F · dr. C is oriented counterclockwise as viewed from above.…

A: Given Fx,y,z=yz i +5xz j +exy k  and C is the circle x2+y2=1, z=3. By stokes theorem we have…

Q: Use Stokes' Theorem to evaluate  F · dr  where C is oriented counterclockwise as viewed from above.…

A: The given vector field and region C is as follows.

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A:

Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

A:

Q: 1. Verify Stokes' Theorem for F = (2x - y)i - yz²j - y² zk, where S is the upper half surface of the…

A:

Q: The parametric form of the solutions of the PDES Uy + u Uz = 0 , u(x,0) = x is (A æ (s, t) = st + s,…

A: We need to find the parametric form of the solution of the partial differential equation uy+u ux=0 ,…

Q: Use Stokes' Theorem to evaluate F · dr where C is oriented counterclockwise as viewed from above.…

A:

Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

A:

Q: 2) Using Stokes theorem, evaluate pvdr where v= 2y'i– 2x° j+÷k_and the C is the curve of C…

A:

Q: Fdr where C is oriented counterclockwise as viewed from above. Jc Use Stokes' Theorem to evaluate…

A: Consider the given question,

Q: Use Stokes' theorem to evaluate      CF · dr  where C is oriented counterclockwise as viewed from…

A:

Q: SF.dr where F Cxpy;Z)=y and C is the urve of intersection of yz=2 antd th 4he sylinder x?ayL with…

A:

Q: Let F: = . Use Stokes' Theorem to evaluate curlF · dS, where S consists of the top and the four…

A:

Q: c) Use Stokes' theorem to evaluate (zy - u)i– In z j+ (x + z²) k) dr, | where C is the intersection…

A: According To Stokes Theorem∮CF⋅dr=∬S(∇×F)⋅ndS here n is unit normal to the surface.

Q: 6. Use Stokes theorem to evaluate $. F•dr, where F = (-3y² , 4z, 6x) and C is the triangle in the…

A:

Q: Use Stokes' Theorem to evaluate ∫CF⋅dr. In each case C is oriented counterclockwise as viewed from…

A:

Q: 13) De termine the surface area of the spiral ramp parametrized by = u cosQu) i + usin(2v)5 +vk with…

A:

Q: Let F(x,y,2)=(6y,42,6x) a pply stokes' Theorem to eveluate F.dr by finding the flax of ceerl(F)…

A: Given F¯(x, y, z)=6y, 4z, 6x By Stoke's theorem ∮cF.dr=∯s(curl F).n^ds and vertices of triangle are…

Q: Use Stokes’ Theorem to evaluate ∫c F ⋅ dr. In each case C is oriented counterclockwise as viewed…

A: Given: f(x,y,z) = xyi + yzj + zxk C is part of paraboloid z= 1- x2-y2   so, A/c to stroke theoram…

Q: c) Use Stokes' theorem to evaluate $ (xy – y) i – In zj+ (x+ x²) k) · dr, where C is the…

A:

Q: S,F•dr, and C is the triangle, with Use Stokes Theorem to evaluate where F(x,y; =) = (x+ y² )i+ (vy+…

A: Given: Fx,y,z=(x+y2)i+y+z2j+z+x2k and C is the triangle with vertices 1,0,0 ,0,1,0 and 0,0,1 We know…

Q: 11. Let F = (-xy + xz²)i + (4xz + y²)j + e² k. Use Stokes' Theorem to calculate fcF. dr, where C is…

A: We have to find∫cF→.dr→.

Q: Let F = %3D So Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the…

A: Here, the given function is F=xy,5z,4y To use Stroke's theorem: ∫CF·dr=∫∫S∇×F·N^ dA And,…

Q: Jse Stokes' Theorem to evaluate O F. dr where C is oriented counterclockwise as viewed from above.…

A: as per guidelines i answered. Thank you...

Q: The surface z? = x² + y? – 4x + 5 remains unchanged when rotated about the line L in R Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S consists of the top and the four…

A:

Q: Let F = curlF. · dS, where Use Stokes' Theorem to evaluate S consists of the top and the four sides…

A: The Stokes's theorem:                                                 where C is the boundary of…

Q: (2 points) (z, 1) dA = 1 where D is the disk z + y? < 9. Now suppose E is the disk a? + y? < 36 and…

A: we have to use change of variable to find the integral

Q: 2) Given vector Á = r?cos²Øâ, + zsinøâg, and function f = r?cosØ + z, find the followings: a) Div.…

A:

Q: Given a ray r(t) = (0; 0; 0) + t(1; 0; 0), t ≥ 0, and a set of spheres of unitradius and centered…

A: Given ray is rt=0,0,0+t1,0,0, where t≥0. The given ray can be written as: rt=0,0,0+t1,0,0x,y,z=t,0,0…

Q: Use Stokes's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

A: Stroke's theorem:  ∫Fdr=∬ (Curl F) n^dS Curl F=ijkxy2x2yyzy2x2y=iz n^=∇s∥s∥=i^+k^2

Q: Let F < ryz, ry, r'yz Use Stokes' Theorem to evaluate curlF dS, where S consists of the top and the…

A: The given surface is a cube, where the bottom face is not considered. The surface in question has 4…

Q: - Prove Stokes' Theorem by verifying it for F= [y,z,x] and S the paraboloid. %3D te CEY2=(x, y) = 1…

A:

Q: Which of the following are parametric equations of the line of intersection of the planes x+2 z=3,…

A: We have to check

Q: Use Stokes' Theorem to find m # 0 satisfying F · dr = -5, whereF(r,y, z) = (3yx² + z³, y², 4yx²) e C…

A: Given:

Q: Consider the surface S given by: S :r(u, v) = (uv², u + v, v³), u E [0, 1], v E [0, 2]

A:

Q: Use Stokes' Theorem to evaluate F · dr where C is oriented counterclockwise as viewed from above.…

A: Concept Used: ∫CF·dr=∫∫ScurlF·dS Where C is the boundary of the surface oriented counterclockwise

Q: F.dr where C is oriented counterclockwise as viewed from above. Use Stokes' Theorem to evaluate Jc…

A: It is given that F (x, y, z) = xyi+4zj+7yk and the cylinder is x2+y2 = 9.Use the stokes theorem to…

Q: Let C be the curve of intersection of the spheres x? + y + z? = 11 and (x – 2)² + (y – 2)² + z² =…

A: Let C: Curve of intersection of spheres x2+y2+z2=11 and  (x-2)2+(y-2)2+z2=11.Take…

Q: #6. Use Stokes' Theorem to evaluate S. F dr, where F(x, y,2) = i+(x + yz)j+(xy-V) k and C is the…

A: Given that, Fx,y,z=i+x+yzj+xy-zk and C is the boundary of the part of the plane 3x+2y+z=1 in the…

Q: Use Stokes's theorem to evaluate F dr, where F(r, y, z) = ry i+x*yj+yz k, where C is a triangular…

A: Given that, F(x,y,z)=xy2i+x2yj+yzk Using the stoke's theorem, ∮F.dr=∬S(curl f.n)dS Now let's find…

Q: c) Use Stokes' theorem to evaluate + (zy – y) i – In z j+ (r + x*) k) · dr, where C is the…

A:

Q: Use Stokes's Theorem to evaluate EF. dr. In this case, C is oriented counterclockwise as viewed from…

A:

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Given:  F(x,y,z)= 7yi+xzj+(x+y)k To Evaluate: Concept: Stoke's Theorem: Curl:

Q: (a) The part of the surface z = 1+ 3x + 2y² that lies above the triangle with vertices (0,0), (0,…

A: a) Given part of surface is  z=1+3x+2y2, which lies above the triangle with vertices (0, 0), (0, 1),…

Q: F

A: