Check if the following vector field is a conservative field, (do NOT use the curl): F(x, y, z) = (2ry² + 2x22)i + (2xy + z)j + (2rz +y + 2z)k. If it is conservative, what the function whose gradient gives this vector field?

Q: Consider once again the notion of the rotation of a vector field. If a vector field F(x, y, z) has…

A: Question 39 - F(x, y, z) = -sinx, 3y3, 4z+12Curl of F = ijk∂∂x∂∂y∂∂zFxFyFzCurl of F =…

Q: Show that the vector field F(x, y, z) = xz i + xyz j - y 2 k can’t be written as the curl of another…

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Q: Sketch the following gradient vector field, F(x, y, z) = 2xi - 2yj – 2xk. Then find the vector…

A: The given problem is to sketch the given vector field and also to find the gradient of the given…

Q: Determine whether the vector field is conservative.

A: To determine whether the vector field is conservative.

Q: Find the divergence of the vector field F(x,y,z) = (ye*,2x + 3y, ycosx).

A: Consider a vector field is defined as, Fx,y,z=f,g,h The divergence of the vector field is defined…

Q: F = (x² +y², y² +z?,.

A: on solving this we get the

Q: Give an example of a vector field F(z, y) in 2-space with the properties that F is perpendicular to…

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Q: A vector field is described as F = (-z + 7x, x³y²z=1,3x + 2z²). (i) Calculate curl F. (ii) Determine…

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Q: The vector field F is shown in the xy plane. 1 2 Is div F positive, negative, or zero? Positive…

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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: Let F be the vector field (ze"z + yz², xz², xeaz + 2xyz) (a) Find the divergence of F.

A: We will find out the required value.

Q: 2) For the vector field F(x, y, z)=(xz²-x²y)i + (xy²-y³2²)] +xy²z³k, find the following: a) Find the…

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Q: Find the gradient vector field Vf of f. f(x, y, z) = xSye'/z Vf(x, у, 2) %3D

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Q: Determine whether the vector field given by F is conservative. F(x, y) = x2yi + xyj

A: Given vector field: F(x, y)= x2yi + xyj   Concept used: The vector field F = Pi+Qj is conservative.…

Q: determine whether or not F is a conservative vector field. F(x,y)=(y2-2x)i + 2xyj

A: For a  conservative vector field F, curl F=∇×F=0

Q: Is there a vector field Ğ on R³ such that curl Ġ = (xyz,–y*z³,y*z*)?

A: the given function is, G→=xyzi^-y4z3j^+y3z4k^ If there exists a vector field G then the divergence…

Q: For the vector field F = ((y/z2+1)i + (-2x/z2+1)j + (3x2+3y2/(z2+1)2)k , calculate curlF

A: We have given vector field F=yz2+1i+1-2xz2j+3x2+3y2z2+12k=yz2+1,1-2xz2,3x2+3y2z2+12=F1,F2,F3…

Q: Determine whether the following vector field is conservative on an open region R of R2 that does not…

A: For our guidelines answer only  question 2 but I give answer of both questions

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: A vector field is given as F=3x²i – yj + z'k a) Find the streamline of the vector field and also the…

A: Streamline of the vector field is the family of curves which are tangent to the vector field. Curl…

Q: Determine whether the vector field is conservative. F(x, y) = 6y6(yi + 7xj) conservative not…

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Q: Determine whether or not the vector field F(x, y, z) = is conscrvative or not by computing the curl…

A: Solution is given below:

Q: Find the equations of the field lines for the vector field defined by the two dimensional field, F =…

A: Given vector field F=xi^-yj^....(1) Compare the equation (1) with F=dxdti^+dydtj^, we get  dxdt=x…

Q: Given the vector field F(x,y,z) = [x, y, -2z] satisfies div(F) = 0. Find a vector field G(x,y,z)…

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Q: Determine whether or not the vector field is conservative F(x,y) = 18x²y²i + 12x³yj conservative O…

A: NOTE: Refresh your page if you can't see any equations. . compare this vector field with  so here…

Q: Determine whether the vector field is conservative. F(x, у) %3D yi + xј conservative O not…

A: The given function is  fx,y=yi+xj

Q: Show that the vector field F(x, y, z) = (-ycos(8x), 8x sin(-y), 0) is not a gradient vector field by…

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Q: Verify Stoke's Theorem for the vector field F = (2y + 2) i + (x –2)ĵ+(y – x) . over the portion of…

A: The formula for stokes theorem is, ∫Pdx+Qdy+Rdz=∬∇×F.ndS Given that, F=(2y+z)i+(x-z)j+(y-x)k Then,…

Q: Find the curl and the divergence of the vector field. F(x, y, z) = x²yzi - x³y k i + Submit Answer…

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Q: The divergence of the vector field F(z, y, z) = (ya°, az", zy?) is: %3D

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Q: Determine whether or not the vector field is conservative. If it is conservative, find a function f…

A: Given a vector field, Fx,y,z=ye-xi+e-xj+7zk. By the component test for conservative fields, Let…

Q: Determine if F(x, y, z) = (z! + z In y, z + z ln x, y ln x + x In y + z²) is a gradient vector…

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Q: Consider the given vector field. F(x, y, z) = (In(x), In(xy), In(xyz)) (a) Find the curl of the…

A: Given vector field: F(x,y,z)=ln(x),ln(xy),ln(xyz)

Q: b) Verify whether the vector field F is conservative, if so, then find the potential function F = ,…

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Q: Find a vector field with twice-differentiable components whose curl is x i + yj + z k or prove that…

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Q: Consider the vector field F(z, y. 2) = -3yzi +(-3rz +2yz²)j+ (-3zy+ 2y°z + 1)k. (a) Calculate curl F…

A: Note: As in the part (B) the page 94 is missing, so we are solving one (a) part of the given…

Q: Explain why Green’s Theorem proves that if gx = ƒy,then the vector field B = ⟨ƒ, g⟩ is conservative.

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Q: The vector field F is shown in the xy plane and looks the same in all other horizontal planes. 3- Y…

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Q: Determine whether F(x, y) = 6x²y i+ 4xy²j is a conservative vector field. If so, find a potential…

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Q: Determine if the vector field F is conservative. F=xyi + yj+zk Conservative Not conservative

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Q: Determine whether or the Vector Field is Conservative. If it is conservative, find function f such F…

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Q: Give an example of a vector field F (x, y, z) that has value 0 on precisely one line and such that…

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Q: Determine whether or not F is a conservative vector field. F(x, y) = (my + ²)i + (mx + 7);

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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: Let F(x, y, z) = xyi + y²j, find divergence and curl of vector field F.

A: The divergence and the curl of a vector function, f(x,y,z) are defined as…

Q: Give an example of a vector field F (x, y, z) that has value 0 at only one point and such that curl…

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Q: Determine whether the vector field is conservative. 7x², F(x, y) = Yi + conservative O not…

A: If curl f is zero then vector field is conservative otherwise not

Q: Choose the option in which the vector field is conservative. Select one: F =(xy,x+y> F = (2xy² -…

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