How many of the following vector fields are NOT conservative? F= xyi + yj + zk F= - cos x cos yi + sin x sin yj - seczk F=-i- 5j-k 2. F = (y - z)i + (x + 2y – z)j – (x + y)k O 2 O 1 3 OLO

Q: Given the vector field E = 4zy² cos 2xa, +2zy sin 2xay + y² sin 2xa₂ for the region [x], [y], and…

A: The general form of a vector-valued function in three dimensions is given by F=F1ax+F2ay+F3az, where…

Q: 5. Consider the vector field F(x,y,z) = yzi + xzj+(xy+2z) k and the curve C given by r(t) = (t+ sin…

A: Given vector field: Fx,y,z=yzi+xzj+xy+2zk Curve C is given by: rt=t+sin12πt,t+cos12πt,2t,   0≤t≤1…

Q: Which of these is a conservative vector field given that all fields are open and simply-connected?…

A: We are given that all fields are open and simply connected. We have to find out which of the…

Q: 1: Which of the following vector fields are conservative? (i) F(x, y) = (9x*y8 + 6) i + (8x°y7 + 4)…

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Q: If F =  P i + Q j + R k is a vector field on R  3  and aP/ax , aq/ay and  ar/az exist, hen the…

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Q: 13 Given the conservative vector field, F = (x +3y?)i +(6.xy +5)j , evaluate the 120) integral F.ds…

A: Here we use the way of line integral. By finding the parametric path between two points.

Q: Find the curl of the vector field F(x, y, z) = e" sin yi – e" cos yj O -2e" cos yk O -2e" cos y O…

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Q: 4. consider F(x, y) = (y² − 2xy) i + (2xy − x²) j. (a) Show that F is a conservative vector field in…

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Q: Could the following vector field. F. be conservative F(z,9) = (6z" cos (y), 4y²cos (z)) Select the…

A: Given vector field Fx,y = 6x4 cos(y), 4y3 cos(x)

Q: 3. The vector field F(x,y, z) = (-27x sin(rx² + z), 2ye"",– sin(rx² + 2) – 2) is conservative. Let C…

A: (3)Given:-Fx,y,z=<-2πx sinπx2+z,2yey2,-sinπx2+z-2> is conservative.To find:- ∫C F.dr  where C…

Q: 7) Consider the vector field F (x, y, z) = (xZ + cos y, XZ - x sin y, Xx). The work that the F field…

A: A) 10,57 J

Q: The conservative vector field: F = (2ry- z, r + 2z, 2y – 2rz). has potential function O 0 - 2y 212…

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Q: Find the Curl of the vector field. F(x,y, z) = 7e" sin(yi+ 8e* cos(y j+ 14z k a. &e" cos(y) +7e"…

A: solution of the given problem is below...

Q: Which one of the following is a potential function of the following vector field? O f(x,y) = xy+2x O…

A: Find potential function

Q: 3. Verify the circulation form of Green's Theorem for the vector field F(x,y)=xyi +2y and the region…

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

A: Here we use polar form of circle .

Q: Find the Curl of the vector field. F(x,y, 2) = 1le sin y i+ 12e* cos(y j+3z k a. (12e* cos(y) +1le"…

A: Curl of a vector can be calculated by forming a matrix and then finding the determinant of the…

Q: 5. Given the vector field F(x, y, 2) = (2x In y|+ 2°|2yz) find the following a. Gradient of . b.…

A: As per Bartleby guidelines, for more than three sub-parts asked for a question, only three is to be…

Q: Which of the following cannot be a conservative vector field? O H) None of these C) F = ( z In y,,x…

A: If a three-dimensional vector field F(p,q,r) is conservative, then py = qx, pz = rx, and qz = ry…

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: Determine whether the following vector field is conservative on R. F-(2 + 3xy 3y +2y) Is F-(2x + 3xy…

A: Explanation of the answer is as follows

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

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Q: Which of the following vector field is not conservative? a) Å(r, y) = yi- 3ryj b) 72r + 14(x² +…

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Q: If a vector field F (x, y, z) = (y² + z², xe cos z, - xe³ cos z), which of the following values is…

A: Given vector field is Fx, y, z=<y2+z2, xey cosz, -xey cosz>.   To Find: div F.

Q: 9. Show that F is a conservative vector field and use this fact to evaluate f F dr along the given…

A: Given information: Fx,y=y2i+x2j C is the arc of the parabola y=2x2 from (-1,2) to (2,8). Gradient…

Q: Determine the divergence of these vector fields: (a) P = xʻyz a, + xz a, (b) Q3D p sin фа, + p'za,…

A: The given problem is to find the divergence of the given vector fields, We have to use Cartesian ,…

Q: 5. Show that F =(y cos(x),sin(x)+ y) is a conservative vector field and use this to calculate the…

A: Given: F → = y cos(x), sin(x) + y. A vector field F→ = P, Q is said to be conservative if partial…

Q: A vector field with component form F(x, y, z) = (P(x, y, z), Q(x, y, 2), R(x, y, z)) on R³ is…

A: Given that Fx,y,z=excosy,e-xsiny,2 The objective is to show that F is conservative. So to show that…

Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = J 8 by using…

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Q: The circuitation of the vector field F(x, y) = (x- x'y, xy) along the boundary of {(x, y) ER: x + (y…

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Q: reply as soon as posible.

A: To find out the conservative.

Q: Show that F is a conservative vector field and use this fact to evaluate  F. dr along the given…

A: For a vector field of the form F=Pi^+Qj^ to be a conservative vector field, it should satisfy the…

Q: 2. Which of the following statements are true for all vector fields, and which are true only for…

A: according to our guidelines we can answer only three subparts and rest can be reposted.

Q: 3. Determine if F = x*yi+ xyz j + x²y² k is a conservative vector field.

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Q: Q4. A vector field F is defined as F = psin pa,+ 2p² zas + zcos oa,. The V × F at point P(1, 7/2, 2)…

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Q: Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous…

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Q: 1).Evaluate ∮CF•dr, whereF=⟨e^x−y^3,cosy+x^3⟩, and C is a circle of radius 2, centered at the…

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Q: Find the Curl of the vector field. F(x,y, 2) = 3e" sin(y)i+ 7e* cos(y)j+ &z k cos (y)i+ &z k. %3D…

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Q: (10) Given that the vector field F= 2z i- 3 x j + 4 y k Evaluate f F. dr where S is the portion of…

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Q: (5) Consider the following vector field F (1, y, 2) = yz cos (ry) i+ az cos (ry)j+ sin (xy)k (a) Use…

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Q: 7. Choose an option in which the vector field is conservative: None of them OF = (xy, x+ y) O 2,…

A: A vector field F=∇f is conservative if and only if ∂M∂y=∂N∂x

Q: Find the divergence of the vector field F(x, y, z) = In(x² + y?)i+ cyj+ ln(y² + z² )k 2x + x + 2z x2…

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Q: Show that the vector field F = 2.xyi +(x² – 2 y)j is conservative and evaluate the line integral…

A: Given the vector field

Q: Determine which of these vector fields are conservative. If a vector field is not conservative,…

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Q: Which one of the following vector fields is conservative? O F(x, Y, z) = (xy +1, a²y? – 2, xyz)…

A: 1) fx,y,z=xy+1,x2y2-2,xy2 Let fx,y,z=xy+1   yx,y,z=x2y2-2 hx,y,z=xyz The curl of Fx,y,z = ∇xFx,y,z…

Q: The vector field F(r, y) = (2xy +y) dx + (æ + 2xy) dy is conservative. %3D The function f(x, y) = x²…

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Q: 18. Which of these is a conservative vector field given that all fields are open and…

A: A vector field is said to be a conservative vector fieldif it is equal to gradient of some scalar…

Q: #7: Consider the following vector field. F(x, y, z) = 3yz In xi + (9x – 6yz)j + xy°z³ k %3D (a) Find…

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Q: ermine whether the vector field F(x, y, z) = (x³, 3zy², y³) is conservative on R³. If so, find a…

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