Use Stokes' theorem to compute the circulation OF. 2x + 3y + z = 6 in the first octant. Here C is positively oriented with respect to the plane whose orientation is upward. 25 F. dr where F = (2xyz, 7y²z, 4yz) and C is the boundary of the portion of the plane X

Q: Write a parameterization r(u, v) for the given surface. Include reasonable bounds for u and v. 10…

A: #10 6x+3y+4z=10→4z=−6x−3y+10→z=−23​x−43​y+25​Letx=u∈Ry=v∈RThenr(u,v)=⟨u,v,−23​u−43​v+25​⟩ #11 We can…

Q: Use Stokes' Theorem to evaluate of intersection of the plane .x+3y + 5 = 24 with the coordinate…

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Q: Use Stokes' Theorem to find the circulation of -> F = 3yi + 2zj + 2xk around the boundary of the…

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Q: Calculate F· dS where F = (4x*z, 4y°z, 3:*) S is the surface of the solid bounded by the hemispheres…

A: Given

Q: -Determine the equation of the trace of this plane in the xz plane given 2x + y − z = 4.…

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Q: the z-axis and above the x-y plane. Use Stokes' Theorem to calculate the circulation of F = (x + y?,…

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Q: Use Stokes' Theorem to evaluate ff curlF. ds. F(x, y, z) = 2xyi + 3yzj + 3z²k; S is the part of the…

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Q: Use Stokes' Theorem to find the circulation of F = 5yi + 3zj + 6xk around a circle C of radius 7…

A: Stokes' Theorem: The formula for Stokes' Theorem is given by:         ∫CF→·dr=∬RCurl F→·n→ dA where…

Q: Let F = yi+zj + xk and C is the boundary of the surface S, which is the paraboloid z = 1 - (x² +…

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

A: Given: Fx,y,z=xyi+3zj+6yk C is the oriented counterclockwise. Also C is the curve of intersection of…

Q: Calculate F. dS where F = (4x°z, 4y*z, 32*) S is the surface of the solid bounded by the hemispheres…

A: Given that F→=(4x3z, 4y3z,3z4) and S is bounded by z=16-x2-y2, z=1-x2-y2, z=0 Now,…

Q: Let F(x, y, z)=z²i+ 2xj+y°k and let S be the graph of z = 4-x² -y², z 20 oriented counterclockwise.…

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Q: Use polar coordinates to evaluate || (2x-3y) dA, R ere R is the region in the upper half-plane…

A: Consider the given information.

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: Verify Stokes' Theorem if F(x, y, z) = (x – y)i + (y – z)j+ (z – x)k and S be the portion of the…

A: Solution: The objective is to verify the Stokes theorem for the given problem

Q: Which of the following are parametric equations of the line of intersection of the planes x+2 z=3,…

A: We have to check

Q: Evaluate f. F dS where F(x,y, z) = (4x³z, 4y³z, 3z*) and S is the surface of the solid bounded by…

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Q: Calculate F. dS where = (4e°z, 4y°z, 324) F: S is the surface of the solid bounded by the…

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