3 - 2+ +++ 3 ++ 1/1 2.

Q: Determine the divergence of vector field E = 3x²x + 2zŷ + x²z2 at (2, –4, 0).

A:

Q: How do you graph the vector field F = ⟨ƒ(x, y), g(x, y)⟩?

A: Given: vector field

Q: The vector field F is shown in the xy plane. 3- 2- 2 3 4 Is div F positive, negative, or zero?…

A: Divergence is a operator which operate on vector field F to gives a scalar quantity . And divF is…

Q: When is the vector field continuous?

A: given,       Continuous vector field .

Q: Sketch the vector field F =

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Compute the curl of the vector field F = - (x + 3y) i + (y – 3z) } – (z + 3x) k curl

A:

Q: Explain how to compute the curl of the vector field F = ⟨ƒ, g, h⟩.

A: Here given

Q: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

A:

Q: What is the divergence of the vector field f = x²i+ xyzj – zk at the point (1, 2, 3). Select one: а.…

A: f=x2i+xyz j-zK at (1,2,3)  div f=i ∂f∂x+j.∂f∂y+K.∂f∂z

Q: Consider the vector field F(x, y) = yî- xî+ zR and path joining (1, 0, 1) and (-1, 0, 1) as C;:…

A:

Q: 3) Sketch the vector field F. F(1, y, 2) = yi

A: F(x,y,z)=yi

Q: Consider the vector field F (x, y, z) = (y - zsinx, x, 2z + cosx). The work that performs the F…

A: Given that, F(x,y,z)=y-zsinx, x, 2z+cosxA body is displaced from point A(3π,-1,1) to point Bπ,2,0

Q: Show that F = (2xy + z³)ï + (x²)j+3xz²k is a conservative field. Find the scalar potential and the…

A: Given F = 2xy+z3 i ; x2j + 3xz2kThe objective is to show that given vector fieldis coonservative…

Q: 6. Use Green's Theorem to find the work done by the force field F = ( 2xy, x² + x ) on a particle…

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Q: 3 , find a potential function for the vector field F by inspection or show that one does not exist.…

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Q: Sketch and describe the vector field F (x, y) = (-y,2x)

A: The given vector field is F→x,y=-y,2x A vector field F→ in ℝ2 or ℝ3 is an assignment of a…

Q: Show that the vector field F = 2xyi + (x - 2 y)j is conservative and evaluate the line integral %3D…

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Q: 1. Give an example of a vector field F(x, y) in 2-space such that F has constant direction but || F…

A: The solution are next step

Q: b) Find the curl of the vector field, CurlF, if F= Axzi- By 2j+ Cx tk, %3D where the coefficients A,…

A:

Q: The vector-valued function F (x, z) = (2 − x)i - Tx² kis an example of a vector field in the xz-

A: Given vector valued function F(x, z)=(2-x)i-πx2k

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: 3. Let F be the vector field (ze²z + yz², xz², xe*z + 2xyz)

A:

Q: Compute the flux of the vector field (x2, - xy*), out of the rectangle with vertices (0,0), (4,0),…

A: Given,

Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

A:

Q: Match the vector field with its graph. F(x, y) = yi -5+ -5+

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Q: Sketch the vector field. F(z, y) = (- 2 2 2 0 2 -2 0 -2 2 -2 2 -2 -2 2 -2 4- -4 -3 -2 -1 2 3 -2 -3-…

A:

Q: Find the divergence of the vector field F div F -6z sin (a + 7) %3D

A:

Q: Show that the vector field F(x, y, z) = (2y cos(-3x), –3x sin(2y), 0) is not a gradient vector field…

A:

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

A:

Q: What is the divergence of a vector field? How can you interpret it?

A: Divergence of a vector field:

Q: Compute the flux of the vector field F(x,y, z) = yi– 2xyk over the triangle T with vertices (1,0,0),…

A:

Q: Find a potential function for the vector field F by inspection. F = (4x, 4y) Ф(х, у) 3

A:

Q: Calculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to…

A: To find the line vector of following vector fieldF→=-3i+2jalong the line 4,0 and 12, 0

Q: (b) Verify Green's Theorem for a vector field F(x,y) = xy²i – yx²j on a disc with center (0,0) and…

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Q: Find the curl of the vector field F=(2xyz, -xy,-z^2)

A:

Q: Calculate the line integral of the vector field F = -2i+ 4jalong the line from the point (3,0) to…

A:

Q: Compute the flux of the vector field (x3, – xy³), - out of the rectangle with vertices (0,0), (3,0),…

A: Given: F=x3 ,-xy5with rectangle with vertices (0,0) , (3,0) , (3 ,2) , (0,2) To find flux of vector…

Q: Sketch the vector field F(x,y)=1/2xi-1/2yj at points (-1,1),…

A: Put each given points in F and find subsequent coefficients of vector F to find (x1, y1) Plot the…

Q: Sketch the vector field F(x, y) = (0,–y) Sketch the vector field F(x, y) = (-y,x).

A: (a) The given vector field is: F(x,y)=0,-y Which means, Fx=0; Fy=-y The magnitude of the vector…

Q: How much work is required to move an object in the vector field given as F = yi+3x j Along the lower…

A:

Q: Prove that F = (y' cosx+z')î +(2ysin x-4)ĵ+(3xz² +2)k is a conservative force field, find its scalar…

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Q: Calculate the divergence and the curi of the following vector field at the point (1. 2. 1) Fix, y,…

A:

Q: xi + yj F(x, y) = k- x² + y2'

A:

Q: Calculate the flux of the vector field F 6i + 2x2j- 2k, through the square of side 4 in the plane y…

A: Given vector field is F→=6i→+2x2j→−2k→ We have to find the flux of the given vector field. The flux…

Q: Find a vector potential field for Ġ = [6xz+x³, –3r²y – y², 4.x + 2zy – 32²], i.e. find F such that V…

A: The solution is below.

Q: The figure shows the vector field F(x, y) = (2xy, x2) and three curves that start at (1, 2) and end…

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Q: Sketch the vector field F(x, y) = (-x − y, x - y) at the points (x, y) where x, y = {−1,0,1}.

A: Consider the given vector field, F→x,y=-x-y,x-y Here we need to sketch the vector field at the point…

Q: The figure shows the vector field F(x, y) = (2xy, x2) and three curves that start at (1, 2) and end…

A: The given field is Fx,y=2xy, x2. We say that a field Fx,y=P, Q is conservative if Py=Qx. Compare…