Evaluate Curlv-ñ, where v = 2xyi + (x-2y)j+xzk and ñ is a unit vector normal to the surface shown in the figure: (i) surface z=i surface y=1

Q: a) Find a vector parametric equation for the ellipse that lies on the plane y – 4x + z = -8 and…

A: (a) Given y-4x+z=−8 and x2+y2=4 Let x=ucosv and y=usinv Then z=−8+4x−y ⇒z=−8+4ucosv−usinv Hence,…

Q: Find a parametrization of the line in which the planes x+ y +z= -2 and x + y = - 3 intersed Find the…

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Q: Q3 Evaluate Curlv-n, where v=2xyi +(x -2y)j+xzk and ñ is a unit vector normal to the surface shown…

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Q: 3/ MATH

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Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u ER…

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Q: 5. Using Stokes' theorem, find I (VxF) ndo, where F yi+xj+(y+z) k and S is the portion of the…

A: We have to find I=∫∫S∇×F·ndσ using Stokes' theorem.

Q: Find the surface area of the helicoid (spiral ramp) with vector equation T(u, v) = (u cos v, u sin…

A: We need to find the area of the surface:r→u,v=ucos v, u sin v, v ; 0≤u≤1, 0≤v≤3π

Q: Find the surface area of the helicoid (spiral ramp) with vector equation F(u, v) = (u cos v, u sin…

A: The area of given helicoid is given by using double integral as follows

Q: A vector R = a →y function is given as A = R° cosøR + ôô – 70sinpâ 2 Asino Evaluate / A · ds over…

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Q: This exercise demonstrates a connection between the curl vector and rotations. Let B be a rigid body…

A: Rules for Cross-Products

Q: Evaluate the surface integral ∫∫H 2yd S where H is the helicoid (i.e., spiral ramp) given by the…

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Q: (a) Find a vector parametric equation for the part of the plane z = -- 5y + 81 that lies above [0,2]…

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Q: 3) Let S be a portion of the surface 3z = 12 – 6x – 3y in the first octant. Suppose that S is…

A: 3z=12-6x-3y divide by 3 z=4-2x-y ⇒2x+y+z=4 clearly it's plane The plane cuts the x-axis at (2,0,0),…

Q: Use Stokes's Theorem to evaluate  Integral of the curve from the force vector:  F · dr. or the…

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Q: (d) The curl is related to the rotational properties of the magnetic flux. With a mathematical point…

A: An irrotational vector field is a vector field that has a curl of zero.  Consider a Vector field for…

Q: S is the surface with parametric equations x = Зи+v, у — Зи-v, z = uv for (u, v) in the region D in…

A: Re-writting given integral in form of parametric equation as,∬F.n…

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: 4. Let F(r, y, z) =-ri+ yj + zk and o be the portion of the surface z = 8x-² - y? that lies above…

A: Given vector field is  F(x,y,z)=43xi+43yj+53zk and also the surface σ is portion of the sphere…

Q: 03. a. If F = (y² + z² − x²)i + (z² + x² − y²)j + (x² + y² − z²)k, then evaluate, SSV × F·n dA…

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Q: The figure in this exercise shows a horizontal layer of the vector field of a fluid flow in which…

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Q: 6. Use the Normal Vector to a Smooth Parametric Surface to find the equation of the tangent plane to…

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Q: Find the flux of the following vector field across the given surface with the specified orientation.…

A: Let r be the vector on the surface of  the cylinder y=6x2 for 0 ≤ x ≤ 4​, 0 ≤ z ≤ 2​.Let's…

Q: Q3 Evaluate Curlv•n , where i = 2xyi + (x – 2y)j+xzk and i is a unit vector normal to the surface…

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Q: Verity Gauss' theorem for the vector feld f (x,y, z)= (y,x,2) on the surface of the sechere with…

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Q: Verify Stokes' theorem for the vector ficld v=x'i+x' yj. C is the boundary of the rectangle whose…

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Q: use a parametrization to find the flux f f s F . n dsacross the surface in the specified direction.…

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Q: Let T be the triangular region with vertices (1,0,0), (0, 1, 0), and (0, 0, 1) oriented with…

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Q: Please make sure its right. calc 3 Find a parametric representation for the part of the plane z = x…

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Q: Find the work done by the vector field (5x + yx, x2 + 3) on a particle moving along the boundary of…

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Q: Let T be the triangular region with vertices (1, 0,0), (0, 1,0), and (0, 0, 1) oriented with…

A: given Velocity field V=4i+4j

Q: The area of parametric surface S which is given by r(u, v) = (u+ v) i+ (u- v)j+ (u+v) k; 0<u< 1,…

A: The solution for the asked question is given as

Q: Identify the type of parametric surface produced by the parametric vector function r(u, v) = (2 sin…

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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: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: ind the flux of the following vector fields across the given surface. Assume the vectors normal to…

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Q: | Let F = (z-y)i+(z+x)j-(r+y)k be a vector field. Verify Stokes' Theorem by computing both a line…

A: Given: F→=z-yi+z+xj-x+yk

Q: Verify F(x,y,z) = (2y + z )î + (x – z)ĵ + (y – z )k taken over a triangle cut from the plane x+ y+z…

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Q: F(x, y) = 5x² yi-2x j Use Green's Theorem to calculate the work done by the force field on a…

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Q: Let S be the upper half of the unit sphere X+y+zwhere Osos2n and 0<0Sa/2. See if you get Curl…

A: Given S is an upper unit sphere x2+y2+z2=1 with an outward pointing normal vector. Suppose…

Q: Use Green's theorem to calculate the work done by the force F(x, y) = xy'i + 3xyj on a particle that…

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Q: Use Green's Theorem to find the work done by the force F(x, y)= x(x + y)i + xy2j in moving a…

A: Force, F(x,y)=x2+xyi + xy2j The path of the particle is given as We are moving on a curve C that is…

Q: Find the area of the surface. The helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v)…

A: We have to find the surface area from the given condition

Q: Use Stokes theorem to evaluate: ∫∫Sc  n⋅(∇×F)dS, where F = 5y i − 5x j + 3⋅x^4⋅y^7 k, n is the…

A: Use Stokes theorem to evaluate:   ∫∫Sc n⋅(∇×F)dS,   where F = 5y i − 5x j + 3⋅x^4⋅y^7 k, n is the…

Q: Use Stokes' theorem to evaluate / (curl F· N) dS for the vector field and surface. F(x, y, z) = 6yi…

A: Answer is mentioned below

Q: See attached photo.  Please provide the flux.

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Q: Q3 Evaluate Curlvoñ, where v = 2.xyi +(x² – 2 y)j + xzk and i is a unit vector normal to the surface…

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Q: Use cylindrical coordinates. Evaluate z dv, where E is enclosed by the paraboloid z= x2 + y2 and the…

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Q: Use cylindrical coordinates. Evaluate z dv, where E is enclosed by the paraboloid z = x2 + y2 and…

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