Verify Stokes theorem for the given surface S and boundary 85, and vector fields F. S = ((x, y, z): z-1-x²-y², z 20), (oriented as a graph) 85- ((x, y): x² + y² = 1) F=+x+(9zx + 4xy)k 16 (91)-08-

Q: Calculate grad div F+ curl F at P(-1, 1, 1) where − = (3xz²)i + (xy)j + (2yz)k. O 7i+ 4j - 3k D-3i -…

A: we will find the required.

Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

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Q: Set V = {(x, y) | x ER, YER}. Define addition of vectors by the rule (x, y) + (x, y) = (y + y',x+x')…

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Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y,…

A: The surface H  is defined by    .The vector field  is given by   .We have to sketch the surface H.

Q: For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in…

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Q: 5. Let F(x, y) = square region with vertices (0,0), (1,0), (1, 1), and (0, 1) oriented…

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Q: Let + y³)%¸ æyz 7 4 F = x² + be a vector field on U = {(x, y, z) E R° | (x, y) + (0, 0)}. Find its…

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Q: Given the 2-D vector field : G(x, y) = (2y)î + (x)j and the triangular curve T : line segments from…

A: Given: G→x,y=2yi^+xj^ Triangular curve T, line segments from point A0,0 to point B4,0 to point D4,2…

Q: 2. For the vector field F(x, y, z) = (x²y, xyz, −x²y²) F(x, y, z)=(x2y,xyz,-x2 y 2 ), find: (a) div…

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Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: (c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given…

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Q: Find the work done by the force field F(x, y) = 2xy³i+ 4x²y² in moving a particle counterclockwise…

A: The work done of a force F→ along a curve r→ is defined by ∫CF→⋅dr→.Since curve is closed in…

Q: Vector Field: F(x,y.z) = (-y, 2rz., x²) and Parametric Curve: r(t) = (21, 31, r> Use the parametric…

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Q: Vector Field: F(x,y) = (xv, 3x, – 2y) and Surface: z = 4 - x - 3 y? Use the normal vector formula to…

A: Given surface z=4-x-3y2

Q: Find a formula F = (F₁(x, y), F₂(x, y)) for the vector field in the plane that has the properties…

A: Answer :

Q: 5. Use Stokes' Theorem (and only Stokes' Theorem) to evaluate ffs curlF - dS for the vector field…

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Q: Calculate the curl of the vector g = (x−y) ax+(y+x) ay, and visualize it. Explain what does "curl of…

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Q: Suppose F 2.xz + 3y²) ay + (4yz²) az. (a) Calculate fLL F dS, where S is the shaded surface in…

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Q: HIf vectors x, y, z, u in the real vector space p (the polynomials) are defined by x(t)=1, y (t)=t,…

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Q: Find the curl of the vector field at the given point. F (x, y, z) = x²zi - 2xzj + yzk, (2,–1,3)…

A: The solution as follows :-

Q: Find the curl of the vector field F(x,y,z)=x^2yi-2y^3zj-3zk.   A. curl F = 2y3i + x2k          B.…

A: Option (c) correct  For detail...go through the solution

Q: A force field (in newtons) is defined by F(x, y) = [ + + x, 1 x² +1 y³ зав where coordinates x and y…

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Q: Recognize a vector field in a plane Sketch the vector field. x | y || F(x, y) = (1/2, − 4 ) 2 2 02…

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Q: Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve that consists of two line…

A: Given that  Fx,y = xy2+2x+1 , x2y - 3y is a vector field. Let C be the curve that consists of two…

Q: Find the Curl of the vector field. F(x,y, 2) = 3e" sin(y)i+ 7e* cos(y)j+ &z k cos (y)i+ &z k. %3D…

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Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: Given two vector fields E = 5xya, + 6(x + 3)a, + 8z'a, D = yza, + xza, + xya, (a) Evaluate C= D+E at…

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Q: Find vector and parametric equations of the plane that contains the two intersecting lines † =…

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Q: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below

Q: 6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z,…

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Q: Let f,g be scalar functions, ủ be a vector function, and assuming sufficient differentiability. Then…

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