2. Find the divergence of the vector field F < 5z cos(r), 7zsin(x), 6z > div F = %3D

Q: Make a sketch of the following vector field. F= (2y.x)

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

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Q: Given the following vector field A=yz a,+4xy ay+yaz Determine the A. Divergence B. Curl

A: We have the vector field A→=yzax+4xyay+yaz This can also be written as A→=yzi^+4xyj^+yk^ Now the…

Q: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

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Q: Find the divergence of the vector field F = ā x7, if r = xi+yj+ zk and ā = 3 i+3j+9k, by first…

A: First of all we calculated the vector F by calculating the vector product of the vectors a and r.

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

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Q: If a vector field F (x, y, z) = (evz-, In (x² z), sin z), which of the following values is equal to…

A: We have to find div F(-1,0,1).

Q: 10. For a vector field F = <2xy + y³, x² + 3xy²+ 2y7 find a function f such that F = Vr.

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Q: Match the vector field with its graph. F(x, y) = yi 1 |||||||||| 三 6 靈

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Q: How do you determine whether a vector field in ℝ2 is conservative(has a potential function w such…

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Q: Find the divergence of the vector field F =

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Q: A) Consider the vector-field F(x, y) = 2xy³i+ 3y²x²j. 1. Show that F is conservative. 2. Find a…

A: The given vector field is  F⇀(x,y)=2xy3i⇀+3y2x2j→ We have to show that F→ is conservative

Q: Find the divergence of the vector field F = div F = %3D

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Q: When is a vector field irrotational?

A: We have to determine when is a vector field is irrotational.

Q: Find the divergence in (2,1,-1) for the vector field FCX₁Y₁² ) = x³y² 2 ² + x ² z 3 + x^²yk

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Q: 3. Find the divergence of the vector field. F = ye2* i+2 ye³j 2.x²

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Q: Make a sketch of the following vector field. F = (-x,2y) %3D

A: We sketch the vector field, we choose  the  points and sketch them.

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: 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: 5. Suppose that the vector field F = is conservative. Find a potential function of the vector field…

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Q: 14. Find the curl of the vector field F = x²i – xevj+ 2xyzk

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Q: (xy³ +3x²y, 3xy² + x²) 2+x ху у,

A: According to question given that Vector Field F⟨xy3+3x2y, 3xy2+x2⟩

Q: Graph the vector field F(x, y)=(-3y, 2x); also find the divergence and the rotational.

A: The graph of the  vector field F=-3y, 2x is as follows

Q: Determine whether the vector field F(x, y) = conservative. yi + xj 1 + xy is

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Q: 1. Determine whether F(x, y) et sin yi + e" cos syj is a conservative vector field.

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

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Q: Evaluate both sides for the field- rectangular parallelepiped X = 0 and 1 Y=0 and 2 and Z=0 and 3.…

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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: If F is a conservative vector field on a region R, how do you evaluate∫C F ⋅ dr, where C is a path…

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

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Q: Find the divergence of the following vector field. F = (2x?yz, - 2xy²z, - xyz²) The divergence of F…

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Q: Find the divergence of the following vector field. (x,y,z) F= 9+ 3x? +y? The divergence of F is

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Q: Find (a) the curl and (b) the divergence of the vector field.

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Q: of the vector field Parye" + around the boun 4. and y = 4.

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Q: Which of the following is the divergence of the vector field F=x,y,z)? none of these 3. -3

A: The correct option is 3rd option .i.e. 3 .

Q: Find the curl and divergence for the given vector field.

A: →Divergence is a measure of spread of vector field at a point.→Curl describes the infinitesimal…

Q: Determine whether the divergence of each vector field (in green) at the indicated point P (in blue)…

A: The divergence is Negative because the vector field line is inwards.

Q: Find the divergence of the vector field F .

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Q: 10. Use the Divergence Theorem and the vector field F = to compute the outward flux from the region…

A: Here we will evaluate the outward flux.

Q: Find the divergence of the vector field F div F II

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Q: Find the divergence of the following vector field. F= (3xyz, - 2xy z, - 4xyz?) %3D The divergence of…

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Q: 3. Show that the vector field F = -C with C> 0, is conservative and find its potential.

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Q: Define the following :- i) Vector Field. #) Piecewise Smooth Curve C

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Q: Find the curl and divergence for the given vector field. 1. Posititve 2. Negative div G 3. 0 4. O…

A: The image of a vector field in two dimension is given To determine it's curl and divergence.

Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: for the ough the box c0,8] x[ 0, 41 x[0,2]. Vector field F =, calculate the totalflex Calculate the…

A: Given:F=z,x,yor, F=zi + xj + yk Thus,    div F=∂z∂x+∂x∂y+∂y∂zor, div F=0

Q: 4. Given the vector field Č = p² sin o a, + (z² cos – 1)as + (p² – z)a, Determine the x-component of…

A: Given the vector field