1- xy xy?+1 A) F(r,v) = (", -) B) F(x, y) = (cos(æ – y) – y sin(x – y), y sin(x – y)) C) F(x, y) = (- sin(2a² – 2y), x sin(2a² – 2y)) 2x 2y D) F(x, y) = y² + 1' x² + 1

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: The gradient vector field of for,y)= In +2y) is 2. T True A False

A: The gradient vector field of a function, is defined by the formula below. , where are the partial…

Q: Sketch the following gradient vector field, F(x, y, z) = 2xi - 2yj – 2xk. Then find the vector…

A: The given problem is to sketch the given vector field and also to find the gradient of the given…

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

A:

Q: If a vector field F (x, y, z) = (evz-, In (x² z), sin z), which of the following values is equal to…

A: We have to find div F(-1,0,1).

Q: Compute the curl of the following vector field. F= (3z sin y, 3xz cos y, 6xz sin y) The curl of F is…

A:

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: 10. For a vector field F = <2xy + y³, x² + 3xy²+ 2y7 find a function f such that F = Vr.

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Q: What is the value of a so that the vector field F(x.y)=(In y+2xy³) i+(ax²y2+ x/y) j is conservative?…

A: To find: the value of a for which given vector field is conservative.

Q: Show that the vector field F = (x² cos y, e+y) is not a gradient vector field. %3D

A:

Q: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

A:

Q: Consider the vector field F(x, y) = yî- xî+ zR and path joining (1, 0, 1) and (-1, 0, 1) as C;:…

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Q: Let F = 5xyi + 8y² j be a vector field in the plane, and C the path y = 7x² joining (0,0) to (1,7)…

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Q: Match the vector field with its graph. F(x, y) = yi 1 |||||||||| 三 6 靈

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Q: 3 , find a potential function for the vector field F by inspection or show that one does not exist.…

A:

Q: Given the vector field V(x,y)=- Vx² + y² 1 Conceptaulise V(x,y) with a sketch. 2 Is V(x,y) a source…

A: For a two dimensional vector field, F→(x,y)=M, N , the curl is calculated using the formula, curl…

Q: Is the vector field F = y? – 2x², 2xy + 3| conserva Yes No yz Is the vector field F y? – x2 con Vy?…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: 9. Sketch the vector field F(x, y) : :(yi — х). Vx? + y?

A: Consider the given filed, Fx,y=1x2+y2yi−xj Further simplify. Fx,y=yx2+y2i-xx2+y2i=〈yx2+y2,-xx2+y2〉

Q: (2) For a differentiable vector field f, which of the following is (are) incorrect? (a) ▼ × (▼ × ƒ)…

A: Since we know Formula a→×(b→×c→)=(a→·c→)b→-(a→·b→)c→

Q: 8. Show that the vector field, -y a² + y?' x² + yj²' ) is not conservative in R³, despite the fact…

A:

Q: 4. Is the vector field F(x, y, z) = (yz, xz, xy) conservative? Justify your answer.

A: Calculate divergence of given vector field. If divergence is zero then field is conservative.

Q: Determine the vector field of F. F(x, y) = 6i – 2j

A: We have to identify the vector field for the given vector.

Q: 5. Suppose that the vector field F = is conservative. Find a potential function of the vector field…

A:

Q: 3 2) Integrarte the vector field hlxry,2)= xyi + ya J+xa k over the twisted cubic PIt)=ti+t?g + t3 k…

A: Given that, the vector field        h(x, y, z) = xy i + yz j + xz k        r(t) = t i + t2 j + t3 k…

Q: 3. Let F be the vector field (ze²z + yz², xz², xe*z + 2xyz)

A:

Q: Four options are shown below. In each of them a vector field. Select the vector field for which path…

A: Here we have to check vector field which is path independent.

Q: Is the vector field F(x, y) = (6ry cos(3x²y + e*) +e* cos(3x?y + e*), 3x² cos(3x²y + e*))…

A:

Q: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

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Q: Find the curl of the vector field F = (4x sin(y), 7y cos(x)). curl F - Dretieur

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Q: 1. Determine whether F(x, y) et sin yi + e" cos syj is a conservative vector field.

A:

Q: Consider the vector field F(2. v) = (--2) i + (8ry° tan ' y) j. i + (8ry² – tan ' y) j. a) Is F…

A: Consider the vector field

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: Consider the following vector field: F = (y* + 1, 3ry + 1). (8.1) Is ſ. F · dr path-independent?…

A: The given vector field is F=y3+1, 3xy2+1. (8.1) For a vector field F=P,Q, the line integral ∫CF·dr…

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)…

A:

Q: Determine if F = (12r – 2x cos y, 2y + x² sin y) is a conservative vector field. If it is, find a…

A: Given that F=(12x3-2xcosy)i+(2y+x2siny)j. We need to determine whether if F is conservative field or…

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: Find g(x, z) so that F(x, y,z) = (8x cos y sin? z + 2e2xz)î – (4x² sin y sin? z)j+ (g(x, z) cos y +…

A: Given that    Fx,y,z=8x cosy sin2z+2e2xz i^-4x2 siny sin2z j^+gx,zcosy+2e2xz k^ Now we have to find…

Q: 3. Find a field F(r,y) (M(r, y), N(r, y)) in the xy-plane with the property that at each point (r.…

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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: Answer True or False: The vector field F(x, y) = (2xe-y,2y – x²e-Y) is conservative. a) True b)…

A: Given that: The vector field, F(x,y)=2xe-y,2y-x2e-y

Q: Compute the curl of the following vector field. F= (5z sin y,5xz cos y, 10xz sin y) The curl of F is…

A: In this question we have to find curl of vector field F

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: Match the vector field with its graph. F(x, y) = xi + 3yj 5 5 5 -5+ -5+

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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: The divergence of a vector field F = 3x² yz? î + 2yz ĵ – xz² k at he point (1,0, 1) is -2 O 2 O 1

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Q: F(x, y, 2) = (y² cos r + 2*)i+ (2y sin æ – 4)j+ (3xz² + 2)k Cos z

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Q: Show that Green's Theorem holds for the vector field F(x, y)=(x +y, 3x) at a square of side 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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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 進 ↑ -6+ <||||||||||| Hex

A: