b) Use Stokes' Theorem to evaluate fF•dr for F(x,y,z) =-yi+ xz j+ zk where C is the curve of intersection between paraboloid z = x? +y² and the plane z=4 with counter clockwise orientation.

Q: Let F = Use Stokes' Theorem to evaluate · dī, where C is the curve of intersection of the parabolic…

A: To find the curl , ∇×F=i^j^k^∂∂x∂∂y∂∂zxy5z7y=i^7-5-j^0-0+k^0-x=2i^-xk^ To find the normal vector,…

Q: 23. Use Stokes' theorem to evaluate Se F · dr, where F(x, Y, z) = (xy, yz, zar) and C is the…

A:

Q: Evaluate the surface integral. || x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: ∫∫sx2yzdS where S is the part of the plane z=1+2x+3y that lies above the rectangle…

Q: 11. Use Stokes' Theorem to evaluate OF dr where F=(xz,e",y+z) on the curve that is the intersection…

A: The equation of curl is F=xz,ey,y+z. The equation of plane is 6x+3y+z=12

Q: Evaluate the surface integral. x dS, S is the part of the plane 16x + 8y + z = 16 that lies in the…

A:

Q: Use Stokes' Theorem to evaluate F dr where F = (x+ 9z) i + (5x + y) j + (7y- z) k and C is the curve…

A:

Q: Let F = < rY, 3z, 4y Use Stokes' Theorem to evaluate | F . dī, where C is the curve of intersection…

A: Here we have, F→=xy, 3z, 4y Using the stoke theorem, we have to evaluate the ∫CF→·dr→=? Where C is…

Q: Evaluate the surface integral. || x²yz ds, s is the part of the plane z = 1 + 2x + 3y that lies…

A: To find ∬Sx2yz dS Here 0≤x≤5  and 0≤y≤2 S→=xi→+ yj→+…

Q: Use Stokes' theorem to evaluate (ry – y) i – In zj+ (r+r²) k) - dr, where C is the intersection…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: Use Stokes' Theorem to evaluate fr F. dr. F(x, y, z) = xy i+ xºj + z² k where C' is the intersection…

A: To find- Use Stokes' Theorem to evaluate ∮CF·dr. Fx, y, z = xy i + x6 j + z2 k where C is the…

Q: 2) Using Stokes theorem, evaluate pvdr where v= 2y'i– 2x° j+÷k_and the C is the curve of C…

A:

Q: Use Stokes' theorem to calculate JJ (A) nds by A = 3yi-xzi+yz²k where S is the surface of the…

A: The given vector field is: A=3yi-xzj +yz2k The surface S is the paraboloid 2z=x2+y2 bounded by z=2.…

Q: 9. Use Stokes' Theorem to evaluate F. dr where F(z, y, 2) = (2 – y) i + (x + 2)j – (x + y) k and C…

A: The given problem is to evalute the contour integral using stokes theorem, where surface C is the…

Q: Use Stokes's theorem to evaluate OF.dr for the given F and C. (c) F(x, y, z) = xzi+ xyj– 3xz k, C :…

A:

Q: 2. Use Stokes theorem to evaluate fs da. a) a = x2 sin z da + y? dy + ry dz, S is the part of the…

A: As per our guidelines, we are supposed to answer only one question and rest can be reposted Given:…

Q: Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xi + yj +Xx² + y² )k and C is the boundary…

A: Stokes theorem: ∮f→·dr→=∬S curl f→·n^ ds Given F(x, y, z)=xi + yj+9(x2+y2)k and C is the boundary of…

Q: (4) Use Stokes' Theorem to evaluate 11. Vx (yz, xz, xy) dS where S is the surface S that is the part…

A:

Q: Use Stokes' Theorem to evaluate SSs curlF · dS, where F(x, y, z) = 7xyi + 3yzj+4z²k and S is the…

A: Consider the provided question, Use Stokes' Theorem to evaluate ∫∫Scurl F·dS,where F(x, y, z)…

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies…

A:

Q: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = xzi+ xyj+2xz k,•. and C is the boundary of…

A:

Q: Use Stokes's theorem to evaluate o F· dr, where F(x, y, 2) = xy² i+x²yj+yz k, where C is a…

A:

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere r2 +y² +2 16 which lies…

A:

Q: Attached picture is the question

A: Consider the provided question,

Q: Evaluate the surface integral. || x²yz dS, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: The surface integral, ∫∫Sx2yz dS, S is the part of the plane z=1+2x+3y that lies above the…

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

A:

Q: 2. Use Stokes' Theorem to evaluate , Vx F ·n dS where F(x, y, z) = and C is the part of the sphere…

A:

Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? be the…

A: Consider the given function. z=x and x2+y2=1 As, the function S be the interior of this ellipse…

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 = . Use Stokes' Theorem to evaluate curlF · dS , where S is the part of the paraboloid z = 14…

A:

Q: Use Stokes' Theorem to evaluate fF.dr if F(x,y,z) =( z-y)i +(x+z)]- (x +y)K and C is the curve of…

A:

Q: Let (S) be the surface given by the following equation. x²+y? = 1+ z?. An equation of the tangent…

A:

Q: Let F = . Use Stokes' Theorem to evaluate curlF · d§ , where S is the part of the paraboloid z…

A: Given: F=-yz,xz,xy To Find: Use Stokes' Theorem to evaluate ∬Scurl F·dS, whereS is the part of the…

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's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

A: Stroke's theorem:  ∫Fdr=∬ (Curl F) n^dS Curl F=ijkxy2x2yyzy2x2y=iz n^=∇s∥s∥=i^+k^2

Q: Use Stokes' theorem to evaluate $ (xy – y) i – In z j+ (x +x²) k) • dr, where C is the intersection…

A:

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

A:

Q: Calculate dS where F = (e* sin y, e" cos y, yz²) and S is the surface of the box bounded by the…

A: We need to find the surface integral. We will need basic knowledge of parametrization of vector…

Q: b) Use Gauss' theorem to evaluate SS F · ndS where F = (x² – y)i + y°z²j+ (xy – yz³)k and o is the…

A:

Q: Use Stokes's theorem to evaluate F dr, where F(r, y, z) = ry i+x*yj+yz k, where C is a triangular…

A: Given that, F(x,y,z)=xy2i+x2yj+yzk Using the stoke's theorem, ∮F.dr=∬S(curl f.n)dS Now let's find…

Q: (b) Use Stokes' Theorem to evaluate (f, curlF .n dS, where F(x,y, 2) = x²yzi + yz?j + z³e™Yk and S…

A:

Q: C is the intersection curve between the paraboloid z = x² + y? and the plane 6x + 8y – z = 21,…

A: Strokes theorem:

Q: Use Stokes' Theorem to evaluate ∫CF⋅dr where F(x,y,z)=xi+yj+3(x2+y2)k and C is the boundary of the…

A:

Q: The surface area of the part of the paraboloid z=x+y that lies under the plane z=2 is: Z=,

A: Surface area is given as A=∬D1+δzδx2+δzδy2dA

Q: Let S is the first-octant portion of the plane 2X+Y+Z=4. Evaluate the surface integral ∬(2Y^2+2YZ)…

A:

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S S is the part of the paraboloid z = 9…

A: Find your answer below

Q: (a) The part of the surface z = 1+ 3x + 2y² that lies above the triangle with vertices (0,0), (0,…

A: a) Given part of surface is  z=1+3x+2y2, which lies above the triangle with vertices (0, 0), (0, 1),…

Q: Let F = · Use Stokes' Theorem to evaluate curi curlF · d§, where S is the part of the paraboloid z…

A: here i had written stokes theorem and done some basic calculation to find the curve of intersection…

Q: Evaluate the surface integral. || x2yz ds, s is the part of the plane z = 1+ 2x + 3y that lies above…

A:

Q: Use Stoke’s Theorem to evaluate the line integral ∮C(z2−y2)dx +(x2−z2)dy +(y2−x2)dz, where the curve…

A: Given equation of the curve is ∮C(z2-y2)dx+x2-z2dy+(y2-x2)dz ,the equation of the paraboloid…