b) Given the vector field F(x,y,z) = 3z cosx i + xlny j + ez tanx k. Determine i. div F, ii. Vx F, UTM iii. grad(curl F) UTM UTM

Q: 4. Is the vector field F(r, y, :) = (yz,rz, ry) conservative? Justify your answer.

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Q: Determine whether the vector field F(x, y) = 5y² (yi+2xj) is conservative. F is not conservative F…

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Q: Determine whether the vector field F(x,y,z)=(y,x,1) is conservative on R° . If so, determine a…

A: Given the vector field Fx,y,z=y,x,1=yi→+xj→+k→.

Q: Consider the vector field F(x, Y, z) = 2xi + 2yj + 2zk. (a) Please compute V × F.

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Q: Calculate the divergence of the vector field. F(x, y) = 3x°i – 2x sin(xy)j div(F) =

A: Given vector function F(x,y)=3X3 i -2x sin(xy) j divF=i∂∂x+j∂∂y+k∂∂z.F

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

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Q: From the given vector field F⃗ (x, y, z) = , compute the curl of F⃗ and find the values of a and b…

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Q: . Consider the vector field F(r, y, 2) = (8r sin y, 4x² cos y – e"z, -e" – sec² z). %3D | F. dR…

A: For a vector field F→, the line integral about the path C is ∫CF→·dr. Let rt be the parametric…

Q: b) Given the vector field SUTM F(r, y, 2) = 3z cos ri+rlnyj+e* tan rk. Determine UTM i. div F, ii.…

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Q: Suppose the vector field F = yi + (x + Z)j + (y + 2z)k is conservative. Find a potential function of…

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Q: ind the flux of the vector field F = yzi + 7yj + yk over the sphere x2 + y2 + z2 = 4.

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Q: 13 Is this vector field F(x, y)=(ycosx)i +(sin x+ y)j being conservative? Please show.

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Q: Determine if the vector field F(x,y)= (x+y,x−y) is conservative? If it is, find its potential.

A: Given Data The vector field is: F(x,y)=(x+y,x-y).   Write the vector field in standard form, The…

Q: 2. Show that V(V × F) = 0, here vector field is twice differentiable. %3D

A: This question is from vectors.

Q: 9. Sketch the vector field F(x, y) : :(yi — х). Vx? + y?

A: Consider the given filed, Fx,y=1x2+y2yi−xj Further simplify. Fx,y=yx2+y2i-xx2+y2i=〈yx2+y2,-xx2+y2〉

Q: Determine if the vector field F=(yz,xz,xy) is conservative?

A:

Q: 13

A: We have to find out conservative or not

Q: 4. Is the vector field F(x, y, z) = (yz, xz, xy) conservative? Justify your answer.

A: Calculate divergence of given vector field. If divergence is zero then field is conservative.

Q: Integrate the vector field h (x, y, =)=ry i+yz j+x k over r (1u) = ui+ j+k, -ןue-L1

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Q: Determine if the vector field F is conservative. F= cos x cos yi + sin x sin yj - sec |- sec zk O…

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Q: Compute the flux of the vector field F = 3xzi + 5yk through the surface S, which is the hemisphere…

A: The flux is given byflux =∫S  F→·n^  dShere,n^=x, y, zx2+y2+z2 in spherical coordinatesF→·n^ =x, y,…

Q: Find the divergence of the vector field F→(x,y,z)=7sinxi→−cos(3y)j→+z^9k→.   Enter the exact…

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Q: Find the divergence of the vector field F = < yx², xzª, zy³ div F =

A: f = y x2  ∂f/ ∂x = 2xy   g = x z4  ∂g/ ∂y = 0   h = z y3  ∂h/ ∂z = y3

Q: Find the work done by the force field F(x,y) = (-y,x) in moving an object along the path y = V4 – x2…

A: Given force field Fx,y=−y,x and object moving along the path y=4−x2  from 2,0 to -2,0. We have to…

Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(V) =

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Q: Determine whether the vector field…

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Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

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Q: Verify that the vector field f is conservative and find its scalar potential. 3r f = + yz + 2xz) i+…

A: If the vector field f:ℝ3→ℝ3 is continuously differentiable in a simply connected domain  and curl…

Q: Determine if the vector field is conservative. 1 -) (yi + «j) F(x,y) = 1+ xy, conservative not…

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Q: Зу 1. Given the vector field F(x, y, z) = î+ Vrz j+x cos y - k, find curl F and div F.

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Q: Find the divergence of the vector field F = < ya", xz°, zy* div F

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Q: 4. Show the vector field Vu x Vv, where u and v are scalar fields, is solenoidal.

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Q: Show that the following vector field is conservative and find the potential F(r, y, z) = (2ry, x² +…

A: The answer is given as follows.

Q: ul for the through the box [o,8] x[ 0,41 x[0,2]. vector field f=<z,x, y2, calculate the rotalflux S.…

A: We need to calculate divergence . The formula for divergence for F=&lt;P,Q,R&gt; is ,…

Q: Compute the line integral of the vector field F = (4y, –4r) over the circle z2 + y? = 16 oriented…

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Q: Is the vector field F = [yze"yz, xze#yz, xye"yz] conservative? %3D O Yes O No

A: The vector field is conservative if ∇×F→=0 therefore, find ∇×F→ ∇×F→=ijk∂∂x∂∂y∂∂zyzexyzxzexyzxyexyz

Q: Find the divergence of the vector field. V(x, y, z) = 7e*Yj – 9e*Yj + 8EY²K - div(V) II

A: A detailed solution is given below.

Q: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Determine if the vector field F(x,y,z)= (yz,xz+2y,xy+1) is conservative. If it is, find its…

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Q: F(x, y) = 6xyi + 3y²j is a conservative vector field.

A: Given :F(x,y)=6xyi+3y2j

Q: Find the divergence of the vector field F. F(x, y, z) = In 5x²+ + 10xyj + In( 2y2 + 722)k div F(x,…

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Q: The outward flux of the vector field F=(x,0, z) across the cylinder x + y = 1, for 0<z<1, is %3D…

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Q: Find the divergence of the vector field F = < yx², xz", zy® div F II

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Q: Calculate F=, around the triangle with vertices: (0,0,2), (2,0,0) and (0,2,0). Can you use Stoke's…

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Q: 4- Evaluate the surface integral of the vector field F = [ax, by, cz] over the sphere r² + y² + 2² =…

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Q: Determine whether the vector field F(x, y) = 5y2(yi + 2xj) conservative. F is conservative Fis not…

A: Just check if curl of F Is zero or not.

Q: Suppose a vector field F(x, y) = wai + VEj is conservative. Then construct a potential function ø(x,…

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Q: Determine whether the vector field…

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Q: B) Find the work done by the conservative vector field F (x, y, z) = yzi+xzj+xyk along a smooth…

A: Since, it is given that the field is conservative.

Q: Compute Sc F.d3 for the vedor field in the Cylinder with out ward facing and the surface which…

A: It is given that F→=xi+yj+ezk and the surface is x2+y2=4,1≤z≤5