Find the flux of the following vector field across the given surface Assume the vectors normal to the surface point outward. across the sphere of radius a centered at the origin. where r (xyz) The flux is equal to CType an exact answer.)

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A: Rules for Cross-Products

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Q: 3) Let S be a portion of the surface 3z = 12 – 6x – 3y in the first octant. Suppose that S is…

A: 3z=12-6x-3y divide by 3 z=4-2x-y ⇒2x+y+z=4 clearly it's plane The plane cuts the x-axis at (2,0,0),…

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Q: Let CCR² be the circle with radius 6 centered at the origin. Let F: R² → R² be the vector field…

A: The objective of the question is determine the flux of given F under C

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Q: a vector field ū in spherical courdinate system Express t in the Cartesian coordinate system. U= -…

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Q: Find a formula for the vector field (vectors are shown as line segments, with a dot at the tail of…

A: From the given information.   Observe the given vector field.

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Q: 15. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y+z)k and the surface z = 4x² - y²,…

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Q: Use Stokes' Theorem to find the circulation of the vector field F =7xzi+(4x+5yz)j +5x^2k around the…

A: F=7xzi+(4x+5yz)j+5x2k,andcircle : x2+y2=1,z=4

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Q: 15. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y + z)k and the surface z = 4 – x²…

A: please comment if you need any clarification. If you find my answer useful put thumbs up. Thank you.

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Q: A vector field is defined in spherical coordinates by F(r, 0, 4) = re,r +r sin Oe, + r²es. Select…

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Q: r = 2 on the hemispherical surface defined by 0 ≤ Ɵ ≤ π/2 and 0 ≤ɸ ≤ 2π F = 100cosƟar Verify Stokes'…

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Q: 5) Integrate the vector field h a,y)= y2i+ (2xy-e*)J C parumetrizal by t€ £0, 5 3. over the circular…

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Q: Evaluate the flux, in the specified direction, of the vector field across the surface. F(x, y, z) =…

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Q: Verify Stokes' Theorem holds for the vector field F = yz i + x k where S is the portion of the plane…

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Q: 4. Use Stokes Theorem to find the circulation of the vector tield F around any smoo th, Simple…

A: Stokes theorem ∫CF.dr→=∫∫Scurl F.N→ ds Curl of the vector point function Ff1, f2 f3…

Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…

Q: Calculate the work done by the force: F(x, y, z) = (y — z)î + (z + x)ĵ+ (x + y)k in moving a…

A: Given: F→x,y,z=y-zi→+z+xj→+x+yk→ and r→t=2cost, 2sint, 2sint; t∈0,2π We have to calculate the work…