Let S be the portion of the ellipsoid x² + 4y² + z² = 4 where z ≥ √3x. Suppose that S is oriented so that the unit normal vector at (0, 0, 2) is (0, 0, 1). Let F be a vector field such that ▼ × F = (–√√3y², – 2zy, z²). (V × F) · îndS. Use Stokes's theorem to compute

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Q: 2. (b) Q 3 p sin фа, + p'zag +z cos ф a,

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A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

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Q: of the vector field F across the surface S in the indicated direction. F = x 2y i  - z k; S is…

A: Introduction: The flux of the vector field F is given by the formula, ∮CF.ndS=∫∫∫div(F)dA

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A: A detailed solution is given below

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Q: 2. Find a unit normal vector to the surface x + y +2 = 5 at the point (0, 1, 2). Ans. Û + 2k)

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Q: R2! salve the following D.Erusingundeteminel Gefficints qrvaniation of Paranmatels リー5×

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