Use Stokes' Theorem to find m # 0 satisfying F · dr = -5, whereF(r,y, z) = (3yx² + z³, y², 4yx²) e C is the triangle with vertices (0, 0, m), (0, 2,0) e (4, 0, 0). Consider the counterclockwise direction of the triangle when viewed from above.

Q: Use Stokes' theorem to evaluate (V x F) - dS where F(x, y, z) = -6yzi + 6rzj + 5(x2 + y²)zk and S is…

A: Given that F(x,y,z)=-6yzi^ + 6xz j^+ 5(x2+y2)z k^ Calculating the curl,…

Q: y dV, where B is the portion of the unit ball B = {(x, y, z) : x² +y² + z² < 1} which lies below the…

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Q: Let F = %3| Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z² =…

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Q: 4. Use Stokes’ theorem to evaluate fa F. dr, where F(x,y, z) = (xy,yz, zx), and C is the triangle…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Let F Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the parabolic…

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Q: Use Stokes' Theorem to find the line integral | (17 + 2y°)i + (w + =°)5 +(= + 2r*)k) • dř where C is…

A: Stokes' Theorem: Let S be a oriented smooth surface which is bounded by the curve C (simple closed,…

Q: Use Stokes' Theorem to evaluate fr. F(x, y, z) = xy i+x6j+z² k where Cis the intersection of the…

A: We can solve this using formula of Stoke theorem

Q: Evaluate fs F dS, where F(r, y, z) = (2², xy, z) and S is the part of the paraboloid z = 22 + y?…

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Q: e dV where E is enclosed by the paraboloid z =1+ a? + y", the cylinder a? + y = 3, E Evaluate and…

A: We will use triple integration here

Q: Compute x dS where S is the portion of the plane z=1+x+2y that lies over the square [0, 1] × [0, 1].…

A: We have to find the surface integral ∫sxds.

Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: Use Stokes' theorem to evaluate (ry – y) i – In zj+ (r+r²) k) - dr, where C is the intersection…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: Use Stokes' Theorem to evaluate fr F. dr. F(x, y, z) = xy i+ xºj + z² k where C' is the intersection…

A: To find- Use Stokes' Theorem to evaluate ∮CF·dr. Fx, y, z = xy i + x6 j + z2 k where C is the…

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

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Q: Determine the work done by the force F"(x,y,z)=(x²y,xy). to move a particle along the line segment…

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Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

Q: Use Stokes' theorem to evaluate frotF. ds. F(x, y, z) = xyi + e²j + xy²k; S consists of the four…

A: To find- Use Stokes' theorem to evaluate ∫SrotF·dS, Fx, y, z = xyi + e2j + xy2k; S consists of the…

Q: Compute (VxF). dS, where S is given by x² + y² + (z − 1)² = 2 and z ≥ 0, F(x, y, z) = (-esinzy, x +…

A: The general form of a vector-valued function is given by F1,F2,F3 where F1,F2 and F3 are the scalar…

Q: Evaluate fc F • dr, where F = (z, y2, x) and C is parametrized (in the positive direction) by r(t) =…

A: F=z,y2,x and C is the parametrized by r(t)=t+1,et,t2 for 0&lt;t&lt;2. We have to evaluate ∫CF·dr.

Q: Let F < xy, 6z, 3y Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of…

A: The given problem is to evaluate the line integral using stokes theorem, we have to find the limits…

Q: 2. Use Stokes theorem to evaluate fs da. a) a = x2 sin z da + y? dy + ry dz, S is the part of the…

A: As per our guidelines, we are supposed to answer only one question and rest can be reposted Given:…

Q: Use cylindrical coordinates to evaluate SI vz dv where E is the solid E bounded by the cylinder,…

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Q: Let F = yz, xz, xy > . // curlF dS, where Use Stokes' Theorem to evaluate - x² – y? that lies above…

A: Given that F=-yz,xz,xy The paraboloid is z=8-x2-y2 and z=7 Finding the plane of intersection,…

Q: Attached picture is the question

A: Consider the provided question,

Q: Evaluate the line integral ∫cF⋅dr, where F(x,y,z)=5xi+yj+3zk and C is given by the vector function…

A: we have given F(x,y,z)=5xi+yj+3zk r(t)=(sint,cost,t)=sint i+ cost j +t k⇒dr=(cost i -sint j…

Q: f F - dř where F(1, Y, 2) = (ry°, 1²y, =) Use Stokes' Theorem to calculate where is the paraboloid z…

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Q: Let r(t)=(ln(t), t, (t^2)/2). Find the equation of the osculating plane corresponding to t= 1

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Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

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Q: 2. Use Stokes' Theorem to evaluate , Vx F ·n dS where F(x, y, z) = and C is the part of the sphere…

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Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S is the part of the paraboloid z = 14…

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Q: Find the equation of the plane perpendicular to the curve r(t) = (cos(2t), t, sin(2t)) %3D at the…

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Q: Let F = < 4x + y², 5y + z, 9z + x So F. dī, Use Stokes' Theorem to evaluate C where C is the…

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Q: 1. Compute ff,(V × F) - dS, where S is given by r² + y? + (z – 1)? = 2 and z > 0, and F(x, y, z) =…

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Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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Q: Calculate fc((7x + 6y) i + (4 + 7y) j) · dr where C is the circular path with center (a, b) and…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 6 + x² + y°, the cylinder 2? + y? = 5, and…

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Q: Use the Stokes' theorem to evaluate p Fdr where F = 3yi + yj+ :k and C is the circle r2 + y? = 3 at…

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Q: Find the circulation of F= (xy)i+(yz')j-(2xyz)k around the curve C in the counterclockwise direction…

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Q: Please help solve this. If this can be solved without linear algebra I would prefer to see that…

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Q: Let D = 4xyäx + 4yzäy + 2(x² + y²)āz C/m². Find the total charge enclosed in the rectangular…

A: Given, D=4xyax+4yzay+2x2+y2az  C/m2 0&lt;x&lt;2,   0&lt;y&lt;5,   0&lt;z&lt;3

Q: Use Stokes' theorem to evaluate V ×F· î dS where = (9y²z, 4xz, 2x²y²) and S is the paraboloid z = x²…

A: Step:-1 Stoke's Theorem:- ∬s∇×F→.n dS=∫F.dr Now, given that F→=9y2z, 4xz, 2x2y2 and paraboloid…

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

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 1+ æ² + y°, the cylinder a? + y? = 4, and…

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Q: 2. Use Stokes' Theorem to evaluate curlF.dS whereF = 2y i + 3z j+(z – z) k and S is the portion of y…

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Q: C is the intersection curve between the paraboloid z = x² + y? and the plane 6x + 8y – z = 21,…

A: Strokes theorem:

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S S is the part of the paraboloid z = 9…

A: Find your answer below

Q: Let F = · Use Stokes' Theorem to evaluate curi curlF · d§, where S is the part of the paraboloid z…

A: here i had written stokes theorem and done some basic calculation to find the curve of intersection…

Q: Use Stokes' Theorem to calculate fe F-dĩ, where F = zyi+3=j+5zk, and C is the closed path around a…

A: Here given that F→=xy i^+3z j^+5x k^ and curve C in xz-plane. To find: ∫C F→·dr→ by Stokes' theorem.

Q: Find SS F dS where F(x, y, z) = z i+(3x – 1)j+ yk and S is the portion of the plane x + y + z = 1…

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