If a vector field F = (x+2y+ az)î + (bx-3y-z)i+ (4x + cy +2z) k is irrotational then the value of a, b,c a A. -4,-2,-1 В. -4, -2, 1 С. 4,-2, —1 D. 4,2,-1

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: 4. Two uniform vector fields are F = 2a, +3ā, -5ä,. Find ExF. given by E=-3a +5ā, +2㸠and

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Q: - draw the vector fields . F(xy) = 2xi – yİk

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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: 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: 1) Find the work done by the vector field F(x, y, z) = (x², 4xy³, xy²) on a particle that %3D…

A: Given force is F→x,y,z=x2,4xy3,xy2 Let r→=rt→ be the boundary of the rectangle with vertices  0,0,0,…

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

A: Given the vector field and the points

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: EXAMPLE 2 Show that the vector field F(x, y, z) = 4xzi + 5xyzj – y²k is not conservative. SOLUTION…

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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: A vector field and a point in the vector field are given. Determine whether the point is a source, a…

A: We find the divergence at the point. If the divergence is positive , then the point is a source. If…

Q: If f is a potential function for the vector field F = (1+2ry+2:², -1+², 4x) then the value of f(-1,…

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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: 2 line of the following vector field that passes through the specified point z²k; (2, 1, 3)

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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: (b) The square with vertices (0,0), (1, 0), (1, 1) and (0, 1), and the vector field F = 3x²yi + x³j.

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Q: Find the divergence of the vector field. F(x, y, z)= 6x¹0i-10xy ¹0j O divF(x, y, z) = 60x⁹-100xy⁹ O…

A: To find the divergence of the given vector field.

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: 11) If f is a potential function for the vector field F = (-2y + 2xyz, -2x + x²z, x² y + 8z), then…

A: To find- If f is a potential function for the vector field F = -2y + 2xyz, -2x + x2z, x2y + 8z, then…

Q: a) T: M, → R, where M, is the vector space of n by n matrices over a field, and T (A) = det(A).

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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: If a vector field A(x,y,z)=xz°ex - 2x yzey+2yzez , calculate the curl 7xA at point M(1,-1,-1).

A: A vector-valued function is a rule used to fix a vector to a particular point in space. The general…

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: Sketch the vector field. y F(7,9) = ( - 55) 2' 2 -2 -2 -2 -2 -2 2. 2. 2. 2. 2.

A: The objective is to sketch the given vector field

Q: Match each three-dimensional vector field with the corresponding plot. er トー IHA - (1, 1, 1) O (x,…

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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: 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: Show that F = (3, 1, 2) is conservative. Then prove more generally that any constant vector field F…

A: Given: F = (3, 1, 2) To show: F is conservative. Also to show any constant vector field F = (a, b,…

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: Sketch the vector field. F(z, y) = (- 2 2 2 0 2 -2 0 -2 2 -2 2 -2 -2 2 -2 4- -4 -3 -2 -1 2 3 -2 -3-…

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Q: Sketch the vector field. y F(z, y) = (-2 | 2 -2 -2 2 -2 2 -2 -2 -2 4+ -4 -3 -2 -1 3 -1 -2- -3 -4…

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Q: This is a two part problem. A. Compute the curl of the vector field F = (7yz, 5xz, 3xy). B. What is…

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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: A constant vector field F(r, y, z) = ai + bj + ck is a gradient vector field. True

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Q: If f is a power function for the vector field F = (2xz, −3z, x2 −3y+12z2), then the value of f(−3,…

A: We have F=2xz, -3z, x2-3y+12z2 Now, F=∇f=∂f∂x, ∂f∂y, ∂f∂z=2xz, -3z, x2-3y+12z2 So, ∂f∂x=2xz…

Q: (20) Given the vector field i = (a² – y² + 2xz)î+ (xz – ry + yz)ĵ+(2² + x²)k. Find v x ở and show…

A: Given v→=x2-y2+2xzi^+xz-xy+yzj^+z2+x2k^

Q: 6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z,…

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Q: Let F(x,y,z)=(2xz^2,−2xyz,9xy^3z) be a vector field and f(x,y,z)=x^3y^2z (∇f=(  ,  , )). (∇×F=(  ,…

A: Given:F(x,y,z)=2xz2,-2xyz,9xy3zf(x,y,z)=x3y2z

Q: Compute and sketch the vector assigned to the points P = (0, 8, 8) and Q = (7, 1, 0) by the vector…

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (3, -9, 7)…

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Q: Match the vector field with its graph. F(x, y) = yi y 1信 5 5 y 5 -6+ -5+

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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: 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, y, z) = (yz, x² z², x³ y³), which of the following is curl F (0, –1, 1)? ||…

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Q: This is a calculus 3 problem. Please explain each step clearly, no cursive writing.

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Q: Find the gradient vector field of f(х, у, 2) — е6х + 3у +2:

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