Given F = xi + 2y j + z k and assume that N is the upward directed normal field to the surface S given as the triangular region bounded by the intersection of the plane x+2y+z = 1 with the positive coordinate planes. Evaluate the surface integral IS S F.NdS = -1/6

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Q: Consider the surface integral of the vector field F [xy2, 3x2, x2z]over a surface S, where S…

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Q: 3) Given the vector field F = circulation around the triangle formed by the intersection of the…

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Q: S is the surface defined by x² + y² = 9,0 ≤z ≤ 8. The vector field is F = (1,2, z). Determine the…

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Q: Use a parameterization to find the flux SF-n do of F=2²i+xj-3zk in the outward direction (normal…

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Q: 2. The vector function Ř(u, v) = (sin u cos v, sin u sin v, cos u), (u, v) E [0, 7] × [0, 2m] gives…

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A: note :  As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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Q: 4. Let F(r, y, z) =-ri+ yj + zk and o be the portion of the surface z = 8x-² - y? that lies above…

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Q: Use Stokes' Theorem to calculate rot F dS, where F = ri + yj + rk and S is the surface given by the…

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Q: Consider the vector field F(x, y, z) = (xe² ye²³, -2e²) Let S be the surface defined by {X²+y²…

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Q: Evaluate the integral curves for the vector field F(x, y) =i -i .

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