Assume that S is the disk 2 + y² <4 in the plane z 0 oriented upwards with positively oriented boundary C, and that F = zi + xj+ yk. Compute both of fF dr and s curl F n dS to verify Stokes' Theorem.

Q: Let C be the unit circle in the xy-plane and N a unit outward point normal vector of C. If / (F N)…

A: We have to choose correct option.

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

A:

Q: Let F-yi + xyj+-xyzk and let Σ be the part of the cone z =sqroot(x^2 +y^2(Figure 3) for 0 < x²+ y²…

A:

Q: State the theorem for Surface Independence for Curl Vector Fields.

A: Stokes' Theorem Stokes’ theorem says we can calculate the flux of curl F across surface S by knowing…

Q: Find VX A for the vector A given by A = -yax + x ay Evaluate Ad A de around the curve x² + y²2 = 1…

A:

Q: Let F = (y², x, z²)and S be the part of the paraboloid z = x² + y² with z < 1 and outward facing…

A:

Q: Verify Stokes' Theorem for the given vector field and surface, oriented with an upward-pointing…

A:

Q: Dat

A:

Q: A vector field is given by A(x,y,z)=xyi+2yzj+3zxk. In this multi-part question we will check that…

A: Here, the vector field, A(x,y,z)=xy i + 2yz j + 3zx k. So, the curl A=ijk∂∂x∂∂y∂∂zxy2yz3zx ⇒curl…

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

A:

Q: 6) Use Stokes' Theorem and Theorem 10 in section 16.7 to find § F · dř. F(x, y, z) = (2y, xz, x + y…

A: .C is oriented counterclockwise, and it is the intersection of the plane  and the cylinder .To Find:…

Q: Let r(u, v)= [2ucos(v), 2usin(v), 2] be a parametrization of a surface S, where 0su33,0svS2 T. Then…

A:

Q: A normal vector to the tangent plane for the surface z = , at the point (1, 1, 1) is: y - Select…

A:

Q: 03. a. If F = (y² + z² − x²)i + (z² + x² − y²)j + (x² + y² − z²)k, then evaluate, SSV × F·n dA…

A:

Q: Compute the normal vector to the surface Ф(и,0) %— (и? — 0?, и +0, и — 0) at that point (4,3).

A:

Q: F. Sketch the region onto which the sector r ≤ 1,0 ≤ 0 ≤/4 is mapped by the transfor- mation (a) w =…

A:

Q: Show that if u = u₁i + u2j + uzk is a unit vector, then the arc length parameter along the line r(1)…

A:

Q: A particle moves on a fixed surface in F.(0), which is defined by z = 2xy. During the motion, the x…

A:

Q: Let F = xyi + yzj + zæk be a vector field. Use Stokes' Theorem to evaluate f. F . dr where C is the…

A: Given that,F=xyi+yzj+zxkand the given plane is,x+y+z=1

Q: Let r(u, v)= [2usin(v), 2ucos(v), 2] be a parametrization of a surface S, where 0sus3,0svs2n. Then…

A: Parametrization of a surface

Q: 5. Let S be the union of the three faces of the tetrahedron lying in the coordinate planes with…

A:

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

A:

Q: R(u, v) = (2v + cos u, 2u + sin v, uv)

A:

Q: Compute the curl of the following vector V defined by V(x,y,z) = e(x²+y² +z²) y

A:

Q: ff curl(x²yi - rzk). n do over the closed surface of the ellipsoid 4 16 Warning: Stokes' theorem…

A:

Q: Let r(u, v)= [2usin(v), 2ucos(v), 2] be a parametrization of a surface S, where 0sus2,0svs27. Then…

A: Given surface is  ,

Q: Let F(r, y, z) = ye²i – rzj + cos zk. Compute curl F. %3D

A: