Use Stokes' theorem to evaluate ∬S curl(F) · dS. F(x, y, z) = xyz i + xy j + x2yz k,    S consists of the top and four sides (but not the bottom) of the cube with vertices (±8, ±8, ±8), oriented outward

Q: When the height of the sand in a particular rectangular sandbox is leveled out then the height of…

A: The height of the sand box is proportional to the volume of the sand. When the height is 2.25 in the…

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

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Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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Q: c) Use Stokes' theorem to evaluate F. dr where F = z' i+yJ + xk and C is the triangle with vertices…

A: Stokes theorem is used to find the line integral of the vector point function

Q: 5. Find u-dr for a unit square in the first quadrant with vertex at the origin by Stokes's C theorem…

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Q: II. Evaluate in rectangular form (a + jb) and in polar form (rz0) given: Z1 = -5 + j12,Z2 = 3 + j4,…

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Q: F(x, y, x) = i + 3xj + 2yk And G(x, y, x) = xi - yj + zk. Find the Curl(FxG).

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Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: Prove the polarisation identity for the norm and dot product: for all x; y in R^n,

A: The polarization identity for the norm and dot product states that: ||x+y||2 + ||x-y||2 = 2||x||2 +…

Q: If x has a value of -4, determine if the series converges (absolutely or conditionally) or…

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Q: •11• F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top and four sides (but not the bottom) of…

A: We have to find the ∫∫curlF ds

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: Let FMN be the transformation of the surface. Prove F*dg=d (F*g) gEA (N) = S(N). where

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Q: Show that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line…

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Q: Let F = . Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (7,0,0),…

A: Given that, F→=5x+y2, 2y+z2, 8z+x2 And vertices of the triangle are, 7,0,0, 0,7,0, 0,0,7. To find…

Q: Let F = –9zi+ (xe*z – 2xe*² ) }+ 12 k. Find f, F •dÃ, and let S be the portion of the plane 2x + 3z…

A: Given, F→=-9zi^+xexz-2xex2j^+12k^ and S be the portion of the plane 2x+3z=6 0≤y≤4

Q: Let u = 2i - j, v = 4i + j, and w = i + 5j. Find specified scalar u . v + u . w.

A: We will apply dot product of vectors.

Q: Let F = SOFF Use Stokes' Theorem to evaluate . dr, where C is the triangle with vertices (6,0,0),…

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Q: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below

Q: (b) Use Green's theorem to calculate the circulation of F around the triangle with verticcs (2,0),…

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Q: OJennifer Findley Write an approximate measure for each angle shown.

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Q: Find curl(zi + xj+ yk).

A: Using definition of curl of vector.