Select the irrotational vector field. O A yz î-2xz + xyz k O B. yz î + xz î + xz R OCzî + z2 + yz R O D.y î + (x+z) Î + yk

Q: Is the vector field F(x, y) = 2xy+y 2xy+ xy+y*x x conservative? Select the correct answer below: O…

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Q: a Compute the flux of the vector field i = -2 i + 5j – 4 k through the rectangular region shown…

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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: What is the value of a so that the vector field F(x,y)=(y eX+4xy3) i+(ax?y-4+ e%) j is conservative?…

A: To find  the value of a for which F is conservative.

Q: What is the value of a so that the vector field F(x,y)=[y eX+4xy3) i+(ax3y4+ e%)j is conservative? О…

A: We are asked to find the value of a.

Q: Suppose S is the surface where x? + y? + 3z² = 1. Let F be the vector field F = (xy, yz, z?).…

A: suppose S is the surface where x2+y2+3z2=1 let F be the vector field Fxy, yz , z2 claim- evaluate…

Q: Match each three-dimensional vector field with the corresponding plot. レ 4レ/ / トー / tト44レ O (x, y,…

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Q: Integrate the vector field h (x, y, =) = xy i +yz j+ xz k over r (1) =ui+ử j+ư k, u E[-1,1]. a) 0 b)…

A: According to the given information, it is required to integrate the vector field over the vector…

Q: Two vector fields are F = -10 ax + 20 x (y–1) ay and G = x y ax – 4 ay + z az. For the point P(2,…

A: Given vector fields are F=-10 ax +20 xy-1 ayG=2xy ax -4ay +z azPoint P =2, -3, -4

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

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Q: Integrate the vector field h (x, y, =) = xy i +yz j+xz k over r (u) = u i + ưj+ ư k, и €-1,1]. а) 0…

A: Evaluate the integral of h over r

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: Match the vector field to its graph. 1. 2. = %3D 3. F (x, y) 1 = F (x, y) = F (x, y) 4. E 5.

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Q: What is the value of a so that the vector field F(x.y)=(y eX+2xy4) i+(ax?y3+ e%)j is conservative? O…

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Q: Let F(x,y) = (ax?y +y³ + 1)i + (2x³ + Bxy² + 2)j be a vector field, where a and ß are constants.…

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Q: In the vector field F(x, y) = i + j Compute ||F||. Sketch several representative vectors in the…

A: Given : F(x, y) = i + j

Q: Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is…

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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: Find the curl of the vector field F. F = (x + y - z)i + (5x + y + 8z)j + (9x + 4y + z)k curl F = i+…

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Q: Which one of th e following vector fields is not con servative? A. F (x, y) = (y e*r x e*) B. F (x,…

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Q: Sketch a sample of vectors for the vector field F(x, y) = 4xi + 3yj. Choose the correct answer…

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Q: b) Given the vector field F(x,y,z) = 3z cosx i + xlny j + ez tanx k. Determine i. div F, ii. Vx F,…

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Q: 4) Determine whether the vector field hlxiy)= y?i+ 12xy-e4)T is conservative conservative, deter…

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Q: At how many points is the vector field F(x, y, z) = (z– ,r – 2², y – x²) irrotational? Select one:…

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Q: What is the curl of the vector field F(z, y, z) = ryi+ zyzj + yzk O a. (-ry + z)i + (yz – 2)k O b.…

A: We have to find

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: Find the potential function for the vector field given as 2 F(x.y.?) = Oa. $(x, y, z) =x*y + x²2?…

A: Answer:   The correct option is B.

Q: Given a vector field is conservative. find a potential function 9 for F(x,y,z) = óxi + 4yj+ 1ázk a.…

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Q: Find the flux of the vector field F = through the half-sphere z = V1 - x² - y2. none of these above…

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Q: Find the potential function for the vector field given as 8. F(x, y, z) = 4 O a. $(x, y, z) = x³y³z²…

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Q: 4. Determine whether or not the vector field F(x, Y, z) = (-xye®, -xe + e° + 2y, 2z) is…

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Q: How much work is required to move an object in the vector field F = 5 y² ỉ + 2xy] Along the curve C,…

A: Given: F=5y2i+2xyj  C1 is the line y=0 C2 is the line x=1 C3 is the line segment joining points 1,1…

Q: Sketch a sample of vectors for the vector field F(x, y) = (4x,4y) Choose the correct answer below. O…

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Q: Consider the vector field i = P(x, y) = –3y+ ¤(x² + y² – 1), ý = Q(x, y) = 3x +y(x² + y² – 1) | %3D

A: consider the following

Q: A potential function for the vector field F(x, y, z) = (yz, xz + z, xy + y+ 1) is (x. y, z) = xyz +…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find ||FI|. F(x, y) = i + j Sketch several representative vectors in the vector field. y O O -4 -2…

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Q: Let B(t)-(t,t) be a smooth curve in R. Deter min e a vector field Y =(y- 42) € X(R) with Ya) =(1, 2)…

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Q: For what value of the constant b is the vector field F = bxy'i+x²yj conservative? a. 0 b. 1 4 е. 1…

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Q: (a) Let E be the rectangular prism [0, 1] × [0, 2] × [0,3] and let S denote its boundary region. If…

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Q: o) Find the flux of the vector field F (x,y,z) = 3xi – yj + 2zk; across o where o is

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: a) For the given a vector field A = 3x*yz a, + x*z a,+ (x*y – 2z) a, check whether given vector 'A'…

A: According to the given information, For part (a) Consider a vector field A as:

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

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Q: 1 =(xi + yj + zk) Find the curl of the vector field x²+y? +z? 1 Vx² +y² +z² (예+f+1)- 1 -(i +j+k) x²…

A: Use the formula of determining the Curl F and substitute the values from the vector field. Partial…

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: A. Find the flux of a vector field = 8x i + 6y j+ 2z k through the portion of the plane z = 7 where…

A: As per the guidelines, I am supposed to do the first question only. Kindly repost the second…

Q: Integrate the vector field h (x, y, 2) = xy i+yzj+xz k over r (u) = u i+uj +ưk, u E[-1,1]. a) 0 b)…

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Q: 19. Consider the vector field V(x, y, z) = ( HÓ-DE) 1-y x²+(y–1)² » 2+(y-1)2 and the curves 8 : 2 +…

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Q: Verify if the following vector fields are conservative: 2y 21 a) A1 = (1+æ²+y² > I+x²+y² b) Ã, =…

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