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: 5) By using Stokes' Theorem, find the work performed by the vector field Ex² + 4xy³i+ y²xk,on 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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Q: The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the point A with position…

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Q: Find a unit normal vector of the surface at the given point P. x² + y² = 25, P: (4, 3,6)

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A: The complete solutions are given below

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Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

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Q: -y Consider the vector field F = (y²¹, ²²), and the curve defined by 1% + 2 + 2 = 2 and z = c.…

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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: Find a Vector ū: non zero Vector perpendicular to the

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Q: Show that both R and R2 may be covered by countably many open balls.

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Q: Use Stokes' Theorem to find the circulation of F = 2yi + 3zj + 7xk around the triangle obtained by…

A: Here we have to solve the given problem using stokes' theorem.