Q3 Evaluate Curlv-n, where v=2xyi +(x -2y)j+xzk and ñ is a unit vector normal to the surface shown in the figure: (i) (i) surface z-1 surface y=1

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: A parametric representation of the curve of intersection of the two surfaces x2 + 5y2 - z = 0 and…

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Q: How do you calculate the area of a parametrized surface in space? Of an implicitly defined surface…

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Q: 1. Evaluate the surface integral fs (r + y + z)dS, S is the parallelogram with parametric equations…

A: We are entitled to solve only one question at a time. As the question number is not mentioned, So we…

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: 7) T (u, ) -(υ, 2 cos u, 4sin u). Consider the parameterization With 0, y ve (1,3]. u € describing…

A: Direction of normal always positive y axis. So y component of the normal is positive.

Q: Consider the surface given by x²z+ 2yz2 = 3æy?. %3D (a) Find and (b) Find the tangent plane to the…

A: Surface given, x2z+2yz2=3xy2 ....(i) a)we have to find ∂z∂x  and ∂z∂y  Take equation (i) and…

Q: Find a unit vector normal to the surface x^3- xyz + z^3 = 1 , at the point (1, 1, 1)

A: To find the unit normal vector to the surface x3-xyz+z3=1 at the point 1, 1, 1

Q: A parametric representation of the curve of intersection of the two surfaces x2 + 5y2 - z = 0 and z…

A: The given curves are: x2+5y2-z=0 & z=4y2+36 ⇒x2+5y2-(36+4y2)=0⇒x2+y2-36=0⇒x2+y2=36

Q: ix of F across the surface defined by R(u, v) = (2u, 3v E [0, 1].

A: We have to find the flux according to the given information

Q: ns: Find the tangent plane to the surface of x2 + z² = y² + 9 at (1, –1,3). 3

A: Follow the procedure given below.

Q: F(1)=r cot"(1.4-r')i +1.4(r² -1) j + Jar +1k t = 0 at and is normal to the plane x+y-z 3

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Q: Consider the surface S given by: 4x2 + 4z2 = (1+ y)?, Osys2.Compute: (a) a normal vector at each…

A: Given:-                 Consider the surface S given by: 4x 2 + 4z 2 = (1 + y) 2,0≤y≤2  Compute: (a)…

Q: Consider the surface z = x In y – x²y. (a) Show that Q = (1,1, –1) lies on this surface. (b) Find…

A: Consider the surface: z=xlny-x2y…

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: Find the line integral with respect to arc length (a) Find a vector parametric equation 7(t) for the…

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

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

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Q: 2)Use Stokes' Theorem to evaluate [F.dr where E2xyi, y² j‡ 2xzk and Sis the first octant с surface…

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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: 12. Let C represent the curve of intersection between the cylinder x² + y² = 4 and the plane z = 10…

A: The plane z=10-x will cut the cylinder x2+y2=4 to give an ellipse.

Q: Find a vector normal to the surface x2 + y2 - z² = 18 at P = (3, 5, 4). %3D

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

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Q: A smooth curve is normal to a surface f(x,y,z) = c at a point of intersection if the curve's…

A: Given: A smooth curve is normal to a surface fx,y,z=c at a point of intersectionif the curve's…

Q: Use a parameterization to find the flux do of F = z²i+ xj – 4zk in the outward direction (normal…

A: Apply Divergence theorem to the given surface integral, ∬F.ndσ=∫∫∫DivFdV

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: Use a parameterization to find the flux F•n do of F = z'i+xj- 4zk in the outward direction (normal…

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Q: 1. Consider the ellipsoid (a) Parametrize the surface S = r(u,v) by z = a sin(u) sin(v), y = bcos(u)…

A: Using the parameters on the equation of ellipsoid:…

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

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Q: 3. Consider the parametric vector equation of a cone r(u, v) = u cos vi + u sin vj + uk with 1<u < 2…

A: The volume  of a cone with radius r  and height  h is given by  V=13πr2h.   Given a  function…

Q: Evaluate the surface z =1,0<x,y <1.

A: To solve this we will use divergence theorem.

Q: Find the area of the surface. The part of the surface z = 1 + 2x + 2y2 that lies above the triangle…

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Q: 1. Consider the ellipsoid a?a? + B*y? +v°z? = 7? (a) Parametrize the surface S = r(u, v) by x = and…

A: Given  α=1, β=6, γ=13The ellipsoid α2x2+β2y2+γ2z2=γ2and parametrize the surface S=ru,v…

Q: Find a parametric representation for the surface. the part of the plane  z = x + 2  that lies inside…

A: We need to find parametric representation.

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: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

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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: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

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: 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: iv) Given F (x, y, z) = -yzį + 2xj + xyzk be a vector function that passes through a surface S of z+…

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Q: Verify Green's Theorem in the plane for F = (x² + y²)î + (x² – y²)f in the anti-clockwise direction…

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Q: The spheres x² + y² + z² = a² and (x − b)² + y² + z² = (b − a)² are tangent at the point ○ (−6, 0,…

A: You have posted multiple questions , As per our policies answering first question.