Let F=<-yz, xz, xy >. •[ f, cu S is the part of the paraboloid z = 10 - x² - y² that lies above the plane z = 9, oriented upwards Use Stokes' Theorem to evaluate curlFdS, where

Q: 2. Verify Stokes's Theorem for F(x, y, z) = y i+ z j +x k and the plane x + y + z = 2 in the first…

A: Given, Fx,y,z=yi^+zj^+xk^x+y+z=2 So, curl F is calculating by, Curl F→=∇→×F→Curl…

Q: Show that (u, v) = (6u + 6, u – v, 1lu + v) parametrizes the plane 2x – y – z = 12. Then: (a)…

A: to show = Φu,v=6u+6,u-v,11u+v parametrize the plane 2x-y-z=12 then (A) calculate Tu , Tv , nu,v (B)…

Q: Use Stokes' theorem to evaluate 0 F. dr. F(x, y, z) = zexi + (z − 7y³)j + (x − 5z³)k, C is the…

A:

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

A:

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: F. dr where C is oriented counterclockwise as viewed from above. Jc F(x, y, z) = xyi + 3zj + 5yk,…

A:

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: a) Find the unit tangent vector 7(1), unit normal vector Ñ(t), and unit binormal vector B(t) to the…

A:

Q: c) Use Stokes' theorem to evaluate (zy - u)i– In z j+ (x + z²) k) dr, | where C is the intersection…

A: According To Stokes Theorem∮CF⋅dr=∬S(∇×F)⋅ndS here n is unit normal to the surface.

Q: Verify Stoke's Theorem. F=, C'is the boundary of the paraboloid z = x² + y² lying pelow z = 1 plane.…

A: To verify Stoke's theorem for the below function. F=y,−xz,xz2

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: 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 = . 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: Use Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate…

A:

Q: Show that the tangent plane to the quadric surface at the point (x0, y0, z0) can be written in the…

A: Given surface is x2a2+y2b2+z2c2=1 To find the equation of the plane, find the normal of the given…

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 S be the surface obtained by revolving the plane curve 2x = /9 – y² about the y-axis.

A:

Q: H.W Which of the following vectors is normal to the surface x?yz = 1 at (1,1,1)? (a) 4i +j+17k, (b)…

A: Given the surface is x2yz=1 and (x,y,z)=(1,1,1)

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: Use Stokes' Theorem (in reverse) to evaluate (curl F) ndS where F = 6yzi + 9xj +6yzeªk,S is the…

A:

Q: Use Stokes' theorem to evaluate where = 3x²1+8x³yj + 3x²yk (V x F) - dA and S is the portion of the…

A: Given that S is the portion of the  plane that lies inside the box defined by the .