Let F = < x²ez, rez, 2² ezy > I curlF. S Use Stokes' Theorem to evaluate curlF.ds, where S is the hemisphere x² + y² + z² = 16, z ≥ 0, oriented upwards

Q: The vector equation r (u, v) = = u cos vi+usin vj + vk, 0 ≤ v ≤ 10m, 0 ≤ u ≤ 1, describes a helicoid…

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Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

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…

Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

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Q: Verify the validity of the Stokes's theorem for the vector A = e-bz sin ø a, + pe-bz , over the open…

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Q: Let B be the ball with center at the origin and radius 1 SS $3(x² + y? + z²)dV = B

A: Solve integral by using Cylindrical cordinates

Q: Use Stokes' theorem to evaluate I = ff, Vx F. ds where F = (2²,-3xy, x³y³) and S is the part of z =…

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Q: Use spherical coordinates. Evaluate (8 - x² - y²) dv, where H is the solid hemisphere x² + y² + z² ≤…

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Q: find a unit normal vector to the surface at the indicated point

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Q: Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 3, 0 < v < T…

A: Given that, F¯=y,-x,z5 and ru,v=u cos v, u sin v, v where 0≤u≤3 and 0≤v≤π. Find ru×rv as follows.…

Q: Use Stokes' Theorem to find the circulation of F = 4yi +7zj +3ck around the triangle C' obtained by…

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Q: Determine the parametric equations of the flow lines for the velocity vector field, v, where v =…

A: The given velocity vector is v=yi+xj. To Find: parametric equations for flow lines of the above…

Q: a) Identify and sketch the surface with the given vector equation: r(u,v)=, u between 0 and 2pi, v…

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Q: Let F = Jo Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (10,0,0),…

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Q: Which rays form ZVWX? CLEAR SUBMIT V and X VW and XW WV and WX VWX and XWV

A: Option C is correct option.

Q: Let = In 2r, where r = √² + y². Express V as a multiple of the unit radial vector ê, = ( ) in R2…

A: We are given functionwhere

Q: find the area of triangle between V and W YA (1, 1, 1) V W

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Q: CV4-x2 Va² + yj? dydx 10. Evaluate the integral coordinates. Explain your work. by converting it to…

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Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

Q: 2. Consider the vector-valued function 12t3 – 72t2 + 96t 15t – 60 6t – 24, if t > 0, t + 4, Ř(t = 4…

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Q: Transform to spherical coordinates: F 102-8ỹ+6ż at point P (10, 8, 6)

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Q: eff(V x F) · ds where M is the hemisphere a² + y² + z² = 4, x ≥ 0, with the normal in . M Use…

A: The given problem is to evaluate the given surface integral of the given vector field over the given…

Q: Which of the following is a parameterization for the portion of the elliptical paraboloid octant?…

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Q: True or False: The vector (10, 2, –4) is normal to the surface x2 + y? – 22 = 22 at the point P =…

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Q: Transform the vector C = cospâ – sinpô + cospsinp2 into spherical coordinates and then evaluate it…

A: Given cylindrical co-ordinates system as                                               we know that…

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.

Q: Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N is a vector…

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Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS

Q: Identify the surface by eliminating the parameters from the vector-value r(u.v) = 3 cosv cosui +3…

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