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

Q: a) Find the divergence and the curl of the vector field F × G, where F(x, y, z) = 2x²yi – y³z²j –…

A: Given information: Fx,y,z=2x2yi⏜-y3z2j⏜-2z2k⏜ Gx,y,z=3xyi⏜-5yzj⏜+z2k⏜ The vector field F×G can be…

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.

A: To Find the divergence of the vector field.

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: Find the divergence of the vector field F. F(x, y) = 3xe*i - 9x²y²j

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

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

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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: Find the divergence of the vector field F. F(x, y, z) = In(9x2+ 6y² )i + 54xyj + In (6y? + 5z?)«…

A: To find the divergence of given vector field

Q: Calculate the divergence of the vector field F=x²y³z¹i-xyzj+(x+y+z) k

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Q: Find the divergence of the vector field. F(x, y, z)= 6x¹0i-10xy ¹0j O divF(x, y, z) = 60x⁹-100xy⁹ O…

A: To find the divergence of the given vector field.

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

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

Q: Find the divergence and the curl of the vector field F(x, y, z) = x²yi + 2y'zj+3zk

A: The vector field given is : F(x,y,z) = x2y i +2y3z j + 3z k

Q: find the divergence of the field. F = (x - y + z)i + (2x + y - z)j + (3x + 2y - 2z)k

A: Given Data The field function is fx=x-y+zi+2x+y-zj+3x+2y-2zk.   The expression for the divergence of…

Q: 4. (a) Show that the divergence theorem holds for the vector field F = 2xî + yz} – 3z²k where o is…

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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 field. F= (4x + 5y + 7z)i + (8x - 8y + 3z)j + (2x - 7y + 4z)k div F =

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Q: 10. Evaluate the divergence of the following vector field at the point (0,1,2): F = (xyz, x? + y? +…

A: Given: F=xyz,x2+y2+z2, xy+yz+xz       The point 0,1,2 To find the divergence

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 6x²y²j

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

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Q: b) Evaluate both sides of the divergence theorem for the vector field D = 2xyx + x²9 [C/m²] and a…

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

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Q: xi + yj x2 + y2' F(x, y) = k

A:

Q: What is the flux of the vector field (x2,y2,z1 ) through a cuboid with x ranging from 0 to 8.3, y…

A: use divergence theorem

Q: Find the divergence of the vector field F. F(x, y, x) = i+ zj - 8y²zk %3D O2+ 7- 8y O zi+ 7zj - 8y²k…

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Q: Find the divergence of the vector field F. F(x, y) = 7XEX¡ – 9x²y2j

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Q: Find the divergence of the vector field F. F(x, Y, z) = In( 9x²+ 8y² )i + 72xyj + In(8y² + 7z? )«…

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Q: 9) Find the (i) divergence and (ii) curl of the vector field F(2, y, 2) = (4yz) i+ (y²z) j + (ryz) k

A: We have to find curl

Q: Find the divergence of the vector field F. F(x, y) = 4x²i + 5y²j

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Q: 5. (a) Verify Gauss' Divergence Theorem for the vector field F = yî+x²j– zk and the volume V given…

A: 5.(a)The Gauss' Divergence theorem is,

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

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Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

Q: Find the divergence of the vector field F .

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

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: The divergence of a vector field F = 3x² yz? î + 2yz ĵ – xz² k at he point (1,0, 1) is -2 O 2 O 1

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Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 5x2y²j

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Q: Show that Green's Theorem holds for the vector field F(x, y)=(x +y, 3x) at a square of side 2.

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Q: Let C be the curve of intersection of z = 1 – 2x2 and the cylinder x2 + y2 = 1 oriented…

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Q: the vector field F is shown in the xy plane. y 21 2 Is div F positive, negative, or zero? Positive…

A: Given : The vector field F is shown in the xy plane :   We have to determine that : Is div F…

Q: Q5: Find the divergence of the vector field y F(x, y, z) = x² √yi + =j+zk At the point (2,4,1).

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Q: Find the divergence of the vector field of F(x,y,z) = sinxi + cosy j + z² k. cos x + sin y + 2z O…

A: Option C is correct. To finde divergence I used divergence formula.

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

A: