Let F <-yz, xz, xy > . eff, curlF S is the part of the paraboloid z 8-2²-y² that lies above the plane z = 7, oriented upwards Use Stokes' Theorem to evaluate curlF.ds, where

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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: F · dr  where F  =  (x + 5z) i  +  (7x + y) j  +  (2y − z) k   and C is the curve of intersection of…

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Q: Find the surface area of the portion of the plane z=6-3x-3y which lies in the 1st octant I)2sqrt18…

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Q: Let S be the portion of the plane 2x + 3y + z = 2 lying between the points (-1, 1, 1), (2, 1, −5),…

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A: Given a surface S the normal vector to the surface at the point A is given by

Q: Consider the planes P₁: 3x+y-2zm 7 and P₂ : x+2y+z=4. Give a parametrization for the line of…

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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 L be the line with parametric equations x = 2+t, y = 5-2t, z = 4 + 3t. Let S be the plane that…

A: Given L is the line with parametric equations x = 2 + t , y = 5-2t , z = 4 + 3t . Let S be the plane…

Q: Let ♬ =. Use Stokes' Theorem to evaluate So F. dr, where C is the curve of intersection of the…

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Q: Let F(x, y, z) = -3y² + 4z + 6æk and C is the curve of the intersection of the plane x + y + z = 2…

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Q: c) What is the cosine of the angle between the planes x + 2y – z + 1 = 0, and -x+ 3z + 1= 0? d) Find…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Here use the stokes theorem to find the integral of the function.  And given that the function…

Q: Consider the ellipsoid 4x2 + 2y2 + z² = 27. Find all the points where the tangent plane to is…

A: We have to find the points.

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 F = (y,3z + x,3y² ). Use Stokes' Theorem to find a plane with the equation ax + by + cz = 0…

A: step:- 1 Stock's Theorem:- ∮CF.dr=∫∫SF.n ds=∫∫DF.(rx×ry) dA; D is disk. Step:- 2 Given that   F=y2,…

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: Let F = Use Stokes' Theorem to evaluate с شرح = F. dr, where C is the curve of intersection of the…

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Q: a. Find vectors nį and n2 that are normals to II and IL respectively and explain how you can tell…

A: The planes are given by π1: x1x2x3=0-33+λ11-12+λ2313 and π2: x1x2x3=000+μ112-1+μ2340. For π1:…