3. Stokes theorem x² + y² + z² = 1, Relative to vector field -1 ≤z≤-1/2 F: = (2z, 3x, -y). counterclockwise and draw the graph

Q: b) Given the vector field F(x, y, z) = y² tan 2x i - (lnx) (sin z) j+ey k. Find i. div F ii. curl F…

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Q: Find the curl of the vector field F = (7x sin(y), 3y cos(x)). curl F

A: The given vector field F=7xsiny, 3ycosx. The objective is to find the curl F. Use the derivative…

Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

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Q: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

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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: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: Compute the curl of the vector field F = sin(x) i+ cos(y) j+ 8z3 k

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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: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

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Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: A sphere of radius 1 is x2 + y2 + z2 = 1. Parametrize the sphere as follows:Now,calculate the…

Q: (4) Find a function f such that F = Vf. Consider the vector field F(x, y, z) = y cos(xy)i+(x cos(xy)…

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Q: Show that the vector field F(x, y, z) = (-ycos(8x), 8x sin(-y), 0) is not a gradient vector field by…

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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: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

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Q: 2. Consider the vector field F(x, y, z) = 5zi - 7y3j+5xzk. (a) Calculate div F at the point (1,1,0).…

A: The divergence of a vector field is a scalar function that gives the quantity of a vector field's…

Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below