Given the vector field F (x, y, z) = x²i + 2xy²j¬ +x²zk> a. Find the divergence of the vector field div F→ b. Find the curl of the vector field Curl F

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: Find the divergence of the vector field.

A: To Find the divergence of the vector field.

Q: Given a two-dimensional vector field F and a smooth orientedcurve C, what is the meaning of the flux…

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

A: Given :   To find : a) The divergence of the vector field. b) The curl of the vector field.

Q: Given the vector field F(x,y,z)= , find the divergence and the curl of F. I

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Q: Given a vector field F = 5(x² + y²)i+ 2xyj - 3zk, evaluate SSS, V· FdV for which the solid D is…

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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: For the vector field F(x, y, z) = (15x2y + 2xz)i + (5x3 + 35y4)j + x2k, show that F is conservative…

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Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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Q: Consider the given vector field. 8 F(x, у, 2) %3D (x i + y j + z k) x² + y2 + z2 (a) Find the curl…

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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: Determine whether the vector field F(x, y) = 5y? (yi + 2xj)is conservative. F is conservative O F is…

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Q: Determine whether the vector field is conservative, and, if it is, find the potential function. (If…

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Q: Consider the following vector field. F(x, y, z) = xy²z²i + x?yz?j + x?y²zk (a) Find the curl of the…

A: Given: Fx, y, z = xy2z2 i + x2yz2j + x2y2z k To find: (a) The curl of the vector field. (b) The…

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

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Q: Consider the following vector field F (x, y, z) = yz cos (xy) i+ xz cos (xy) j+ sin (xy)k (a) Use…

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Q: Find the curl and divergence of the vector field. F(x,y,z)=x^2yz i -x x^3y k

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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: Find the divergence of the vector field F. F(x, y) = 7xe*i - 4x²y²j

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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: Determine whether the following vector field is conservative on R3. If so, determine the potential…

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Q: Compute w(v), where w =(x-y)dx+(x+y)dy is a covector field and v = (x/y)d/dx-(y/x)d/dy is a vector…

A: Given: w =(x-y)dx+(x+y)dy  v = (x/y)d/dx-(y/x)d/dy

Q: Find the divergence and the curl of the vector field .F(x, y, z) = 1 (xi + yj + zk).

A: F(x,y,z) =xi +yj+zkx2+y2+z2 it can be written as F(x,y,z) =xi +yj+zkr   where r =x2+y2+z2 divergence…

Q: Find the divergence of the vector field F F(x, y, z) = In(x² + y²) i + xy j + In(y² + z²) k

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Q: Is the vector field F (x, y) = (2xy – y³) î + (x² – 3xy²) ĵ solenoidal, conservative, both or…

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

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Q: Use the divergence theorem to find the outward flux || (F-n)dS, where the vector field is given by…

A: Given that the vector field,

Q: Зу 1. Given the vector field F(x, y, z) = î+ Vrz j+x cos y - k, find curl F and div F.

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Q: Consider the vector field F = (r²y³, x°y?) Is this vector field conservative? Conservative If so:…

A: Given the vector field <x2y3,x3y2>. We need to: i) Check whether the vector field is…

Q: Consider the vector field F = 2xy i + (x2 + 2y) j. Verify the Green's Theorem in the closed region…

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Q: Consider the vector field F = (a*y°, æ°y*) Is this vector field conservative? Select an answer If…

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Q: Find the divergence of the vector field F. F(x, y) 4xe*i 6x²y?j

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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: Find (a) the divergence and (b) the curl of the vector field F(x, y, z) = cos(z)i + 5ysin(5z)j+…

A: Given vector field is  F(x,y,z)=(cosz)i+5ysin(5z)j+2x2zk

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

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Q: Consider the following vector field. F(x, y, z) = xy²z²1 + x²yz²j + x?y²zk (a) Find the curl of the…

A: div F = i∂∂x+j∂∂y+k∂∂zF(x,y,z) curl F = ∇×F

Q: Determine if the vector field F = y ln zi – x ln zj + xyk is a conservative vector field.

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Q: Consider the surface integral of the vector field F= [xy², 3x², x²z]over a surface S, where S…

A: From Gauss divergence theorem, we have ∬SF→⋅dS=∭VdivF→dV   The vector field is F→=xy2,3x2,x2z.…

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: Consider the vector field F = (x*y, x*y? Is this vector field conservative? Select an answer If so:…

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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: Determine whether the vector field is conservative, and, if so, find a potential function. (If the…

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

Q: Given the vector field F(x, y, z) = (2z3 – 4y2 + axy,x² - 8xy – bz, 6xz? –- ay + 4), compute the…

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Q: Find the divergence of the vector field V(x, y, z) = -2e*'i – e³xyj+ 7e%yzk.

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Q: For the vector field F(x, y, z) = 1. a) Find curlE b) Find div E c) State whether or not the vector…

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Q: Given the vector field F(x,y,z)= , find the divergence and the curl of F.

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Q: Use Gauss's Theorem to evaluate fF.ds for the vector field, F = x³ į+ y³ į+z³k, taking S S to be a…

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Q: Find the divergence of the vector field V(x, y, z) = -2xi + (y + 5 cos(x))j+ (7z + e8xy) k.

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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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