6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z, –4x + 2y, -5x + 6z) Determine which vector field is conservative and denote it by F.

Q: If a vector field F (x+ 2y + az)f + (bx – 3y – 2)]+ (4x +cy+ 2z) k is irotational then the value of…

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

A: (a) A line integral is path independent for conservative fields. Hence the statement is true for…

Q: Show that the vector field F(x, y, z) = xz i + xyz j - y 2 k can’t be written as the curl of another…

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Q: Assume that Ax, y, z) is a vector field whose i component is only in terms of y and z, whose j…

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Q: Show that if a vector field has the form F = ⟨ƒ(y, z), g(x, z), h(x, y)⟩, thendiv F = 0.

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Q: 8. Compute the flux of the vector field. F(x,y,z) = (2x -z,-2y, 1-2x) through S= {(x,y,z) € R³: z =…

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Q: 2. Show that for an arbitrary scalar field ø and vector field a (i) V×(Vø)=0 (ii) V.(V×a)=0. (iii)…

A: In vector calculus these derivations have lot of importance. They can be proved very easily and…

Q: Express the vector field B = (x^2- y^2)ay + xzaz in spherical coordinates at ( 4, 30o, 120o) *…

A: Relation between cartesian and spherical co ordinate system x= r sinθ cosϕ   , y = r sinθ sinϕ   ,…

Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F = 6x i + 6y j +…

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Q: Vector fields V and W are defined by V- (2х — Зу + z, -3х — у + 4z,4y + z) W- (2x - 4y — 5z, - 4x +…

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Q: Verify that the work performed along the segment P Q by the constant ~ vector field F = (2, -1, 4)…

A: We have given; vector field F = (2, -1, 4) (a) P = (0, 0, 0), Q = (4 , 3, 5) (b) P = (3, 2, 3), Q =…

Q: Let F(x,y,z)=(−6xz2,6xyz,6xy3z)F(x,y,z)=(−6xz2,6xyz,6xy3z) be a vector field and…

A: Given, Fx, y, z=-6xz2, 6xyz, 6xy3zfx, y, z=x3y2z

Q: EXAMPLE 5 Show that the vector field F(x, y, z) = xz²i + x?yz®j - y*k can't be written as the curl…

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Q: let (x,y,z) be Scalar Field and F a vector field.. $ Derive expression for D. (OF) and * (OF) in…

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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: Determine whether the vector field F→(x,y)=35x4y3i→+21x5y2j→ is conservative.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Evaluate , (V. A) dV for the vector field A = x²yi +xz³j- y²z²kwithin the volume of a cube defined…

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Q: Determine and state the work done by the vector field over the given path in each situation. F…

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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: Given the 2-D vector field : G(x, y) = (2y)î + (x)j and the triangular curve T : line segments from…

A: Given: G→x,y=2yi^+xj^ Triangular curve T, line segments from point A0,0 to point B4,0 to point D4,2…

Q: 3) Determine whether or not the following 3D vector fields are conservative: a) (y²-z³)i + (2xy +…

A: As per the company rules we are supposed to answer only the first question and rest can be reposted.

Q: 5. Compute div F and curl F if F = (2x – cos y)i – x²e32j + (z² – 7x)k. 6. Determine if the vector…

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Q: Find the divergence of the vector field. F(x, y, z)= 7x¹i, 7xy7j O divF(x, y, z) = 7x³¡— Ţxy³j…

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Q: 2. Show that any vector field of the form F(r, y, z) = f(y, z)i + g(x, z)j+ h(x, y)k is…

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Q: Determine the value of k for which (u, v, w) is an orthogonal coordinate system if x = −(u2 + kv2),…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 1. Find the divergence and curl of the following vector fields a. F = (1/y²)j b. F=y³z³i+ 2xyz³j +…

A: We have to find the divergence and curl of the given vector fields.

Q: If a vector field F = (x+2y + az)î + (bx – 3y – z) j+ (4x + cy + 2z) k is irrotational then the…

A: To find the value of a, b, and c if the below vector is irrotational.…

Q: Given the vector field F(7, y, 2) F (x, y, z) = compute the curl of F and find the values of a and…

A: curl(F)

Q: Determine and state the work done by the vector field over the given path in situation. F (x,y) = (x…

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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: Compute the curl of the vector field F = (r“, y^, 25). curl(F(r, y, z)) = What is the curl at the…

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Q: reply as soon as posible.

A: To find out the conservative.

Q: Compute and sketch the vector assigned to the points P = (1, 2)and Q = (−1, −1) by the vector field…

A: A vector field for two dimensional space is defined as a function that gives a vector for each point…

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

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Q: Show that if a vector field has the form F = ⟨ ƒ(x), g(y), h(z)⟩, then∇ x F = 0.

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Q: Let F(x, y, z) = (-7xz²,9xyz, –2ry°z) be a vector field and f(x, y, z) = x°y°z. Vf=( ). V x F =( ).…

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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: Ğ(x, y, z) = (2z3 – 4y2 + Mxy, x2 - 8xy – Nz, 6xz? - My + 4) 1. Find the curl of G 2. Find M and N…

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

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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: Show that V x VG = 0 for all scalar field G(x,y,z). %3D

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Q: 5. Show that there is no vector field G such that: V x G = 2xi + 3yzj – xz?k.

A: Given that ∇×G→=2xi^+3yzj^−xz2k^. We have to show that there is no vector field G→ such that…

Q: 5. Is the vector field F(x, y, z) = (x(z² – y²), y(x² – z²), z(y² – x²)) incompressible? Justify…

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Q: Explain why Green’s Theorem proves that if gx = ƒy,then the vector field B = ⟨ƒ, g⟩ is conservative.

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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: Consider the curve C from (-2, 0, 1) to (6, 5, 2) and the conservative vector field F(x, y, z) =…

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Q: Determine and state the work done by the vector field over the given path in situation. a. i. F (x,…

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Q: A vector field is specified as G = 24xyax + 12(x² + 2)ay + 18z²az. Given two points, P(1, 2, - 1)…

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Q: If a vector field F = (x+2y+ az)î + (bx-3y-z)i+ (4x + cy +2z) k is irrotational then the value of a,…

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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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