7) Consider the vector field F (x, y, z) = (xZ + cos y, XZ - x sin y, Xx). The work that the F field performs to move a body, from point A (0, -T, 1) to point B (2, TT, 2) corresponds approximately to А) 10,57 J В) 14, 57 J C) 41, 70 J D) 33, 70 J

Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (ein z + 2y², 6x + tan¬1…

A: Given force field is F→(x,y,z)=esinx+2y2, 6x+tan-1y, xz Now, we will find the Curl(F→).…

Q: Compute the circulation of the vector field F=(4cos(y))i+(3x^2sin(y))j around C. Where C is the…

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Q: Sketch the vector field F(x, y) = xj, the line segment from (6, 1) to (6,5), and the line segment…

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Q: The curl of the vector field F(x, y, z) = (5z cos(r), 2z sin(x), 72) is: curl F i+ j+ + k Add Work

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Q: 5) By using Stokes' Theorem, find the work performed by the vector field Ex² + 4xy³i+ y²xk,on a…

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Q: Compute the work done by the force field F = in moving a particle along the line segment from (1, 1)…

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Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

Q: Use the Divergence Theorem to compute the flux across the sphere x2+y2+z2 = 1 within the vector…

A: The answer is as follows:

Q: Compute the flux of the vector field F(x, Y, z) = 6i + 5j + 3k through the rectangular region with…

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Q: 4. Is the vector field F(r, y, :) = (yz,rz, ry) conservative? Justify your answer.

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…

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Q: Find the curl of the vector field F→(x,y,z)=e^xsinyi→−e^xcosyj→+xyk→at the point (10,9,24).…

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Q: Determine whether the vector field F(x,y,z)=(y,x,1) is conservative on R° . If so, determine a…

A: Given the vector field Fx,y,z=y,x,1=yi→+xj→+k→.

Q: 3. Use the Divergence Theorem to find the flux of the vector field F = (5x+ 4y?z – 162³) i +…

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Q: Consider the vector field F(x, y) = yî- xî+ zR and path joining (1, 0, 1) and (-1, 0, 1) as C;:…

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Q: Consider the vector field F (x, y, z) = (y - zsinx, x, 2z + cosx). The work that performs the F…

A: Given that, F(x,y,z)=y-zsinx, x, 2z+cosxA body is displaced from point A(3π,-1,1) to point Bπ,2,0

Q: (b) Verify Green's Theorem for a vector field F(r, y) = ry²i – yx²j on a disc with center (0,0) and…

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…

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Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x Y F(x, y) =

A: To find the work done by the force field F in moving an object from P-3, 7 to Q7, 5. Fx,…

Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

A: Outward flux by using gauss divergence theorem

Q: 2. Show that V(V × F) = 0, here vector field is twice differentiable. %3D

A: This question is from vectors.

Q: 8. Show that the vector field, -y a² + y?' x² + yj²' ) is not conservative in R³, despite the fact…

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Q: Determine the work done by the force field F(x, y, z) = (x − y2, y −z2 , z − x2) on a particle that…

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Q: 4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in…

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Q: Find the work done by the force field F(x, y, z) = on particle that moves along the line segment…

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Q: Is there a vector field Ğ on R³ such that curl Ġ = (xyz,–y*z³,y*z*)?

A: the given function is, G→=xyzi^-y4z3j^+y3z4k^ If there exists a vector field G then the divergence…

Q: Integrate the vector field h (x, y, =)=ry i+yz j+x k over r (1u) = ui+ j+k, -ןue-L1

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Q: Find the work done by the force field F(x, y, z) = (x – y², y – z?, z – x2) on a particle that moves…

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Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

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Q: Compute the curl, Vx F, of the vector field. F(x, y, z) = 5xi + 3yj + 4zk %3D curl(F) =

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Q: Is there a vector field G on IR such that curl G = (xyz, -y°z®, y8z®)? O Yes O No Explain. There…

A: Given

Q: Find the work done by the force field F(x, y, z) = (x − y², y - z², z - x²) on a particle that moves…

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Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…

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Q: 6. What is the corresponding vector fieldV for the scalar potential p(x, y)= In(x+ ¥)?

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Q: Compute the flux of the vector field F(x,y, z) = yi– 2xyk over the triangle T with vertices (1,0,0),…

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Q: Compute the flux of the vector field F(x, y, z) = 3x + 3yk through the surface S, where S is the…

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Q: Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x² +…

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Q: Use the Divergence Theorem to find the flux of the vector field F = (3x2 – 3yz + 423) i + (4.xz –…

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Q: There is a vector field F (, y, z) such that divF (x, y, z) = curlF (x,y, z). (M (x, y, z) , N (x,…

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Q: Compute the flux of the vector field F(x, y, z) = 3xj + 3yk through the surface S, where S is the…

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Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: Sketch the vector field F(x, y) = xj, the line segment from (1, 9) to (6,9), and the line segment…

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Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (esin x + 2y², 6x + tan-…

A: We have to find the work done by the force field F→x,y,z=esinx+2y2,6x+tan-1y,xz in moving a particle…

Q: Suppose a vector field F(r, y) = construct a potential function o(r, y). i+ j is conservative. Then

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Q: Show that Green's Theorem holds for the vector field F(x, y)=(x +y, 3x) at a square of side 2.

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Q: Determine the curl of the vector field A = pz sin o ap + 3pz cos o ao at (5, ,1) %3D O-1 O -6pz cos…

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Q: Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

A: Given problem:- Show that the vector field A = (3x²z+ y²)ax + 2xyay + x³az is conservative. =

Q: Sketch the vector field F(x, y) = xj, the line segment from (1,9) to (5,9), and the line segment…

A: To solve the following line integral

Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?

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Q: Find the flux of the vector field F(x, y, z) = [x4, −4yx3, 7z + sin(xey))] through the outwards…

A: