If a vector field A(x,y,z)=xz3ex - 2x2yzey+2yz4ez , calculate the divergence ∇·A at point M(1,-1,-1).

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (7, –9, 5)

A: Given vector field F(x,y,z) =x2 z i -2xz j +yz k   ; (7 , -9 , 5)

Q: The gradient vector field of for,y)= In +2y) is 2. T True A False

A: The gradient vector field of a function, is defined by the formula below. , where are the partial…

Q: Find the divergence of the vector field F <7", 22°, zy* div F -

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Q: Compute the flux of the vector field F = 5xi + 2yj through the cylindrical surface shown below, if a…

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Q: Find the divergence of the vector field.

A: To Find the divergence of the vector field.

Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz2j + 4yz²k; (5,…

A: Recall divergence is a scalar and has formula enclosed in next page

Q: Show that the outward flux of a constant vector field across any closed surface to which the…

A: We have to Show that the outward flux of a constant vector field across any closed surface to which…

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

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

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

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

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Q: Find the divergence of the vector field F(x, y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…

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: 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: Find the divergence of the vector field v = (x²y² - z3)i + 2xyz j + e*yzk. a) 2xy2 + 2xz + xy e*yz…

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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: Find the divergence of the vector field F = < ya®, æ2®, zy* div F = Preview

A: Divergence of F→=yx3, xz6, zy4

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

A: Solution :

Q: Determine whether F(x, y) = xi +9yj is a conservative vector field. If so, find a potential function…

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

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

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Q: Find the curl of the vector field F(x,y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Let the given vector field is :

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 given vector field at point (1,1,1). Insert your answer below. Round to…

A: Fx, y, z=3x2yi+2xz3j+y4k Comparing with F=Pi+Qj+Rk, we get P=3x2y,  Q=2xz3,  R=y4 Now, ∂P∂x=∂3x2y∂x,…

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: Find the gradient vector field (F(r, Y, 2)) of f(x, y, z) = In(4x + 6y + 22) . F(7, y, 2) = (

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

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Q: Given that the vector field F(x, y) = (2x-3y, 2y-3x) is conservative in the xy-plane. If (x, y) is a…

A: We have to find the value

Q: Calculate the divergence of the vector field F (x, y, z)

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

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

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Q: Find the gradient vector field of flx, y, z)=x'y+y%z4+xz6 O V flx, y,z)= (3x?y+z°, 5x³y³ + 4y*zA,…

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Q: Find the divergence of the vector field F. F(x, y, z) = In( 7x²+ 4y² )i + 28xyj + In( 4y2 + 5z2 )k

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

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Q: Show that the vector field F(x, Y, z) = (x² + y²)i – 2xyj is not conservative on R³.

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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: Consider the vector field F(x,y,z)=(−3x^2,8(x+y)^2,9(x+y+z)^2). Find the divergence and curl of FF.…

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

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Q: Find the gradient vector field of f(x, y) = In(2x + 3y) V

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Q: Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

A: Given problem:- Show that the vector field A = (3x²z+ y²)ax + 2xyay + x³az is conservative. =

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

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: 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.