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: Q4: Find the curl of the vector field F(x, y,2) = xJyi +j+ zk at the point(2,4).

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Q: When is the vector field continuous?

A: given,       Continuous vector field .

Q: Sketch the vector field in the plane along with its horizontal and vertical components at a…

A: We shall use MATLAB to plot the given vector field on the circle.  MATLAB CODE F = @(x,y)…

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: Q4: Find the curl of the vector field F(x, y.2) = x*/yi +j+ zk at the point(2,4).

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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: Given the vector field F = (In(x + 2z), xy, xyz). Calculate curl F(-1,1,1).

A: Solution:-

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: d) An open surface F is given by F = {(x,y, z) |z = 4 – x² – y² , z > 0} . Compute the flux of V…

A: V(x,y,z) = <2x+3y,2y+3x,-4z>F={ (x,y,z) : z=4-x2-y2 , z≥0}Consider, g(x,y,z) = z+x2+y2-4…

Q: Compute the curl of the vector field F = (r', y³, z*). curl(F(r, y, z)) = %3D What is the curl at…

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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: Determine the vector field of F. F(x, y) = yi - xj

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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: Given the vector fieldF(z,y)=(y³+422-2)i+(3zy2+2y+2)j. Evaluate the line integral SF-dr from (1,0)…

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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