Find the work done between point 1 and point 2 for the conservative field F. F= (y +z)i + xj + xk; P, (0,0,0). P2(10,5,4) O A. W= 0 O B. W= 90 O C. W= 50 O D. W= 10

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: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

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Q: 4. Is this vector field F(x,y)=(ycos x)ĩ +(sin x+ y)j being the path-independent field? Please show.

A: To check if the given vector field is path-independent field or not. Given:

Q: Show that work performed by a constant force field F over any path C from P to Q is equal to F - PÓ.

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

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: 6. Let F = (x³ sin y, a* cos y). COS (a) Is F a conservative vector field? (b) If your answer to…

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Q: Which of the following functions is a potential function for the conservative vector field F(x, y,…

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Q: 4. Is the vector field F(r, y, :) = (yz,rz, ry) conservative? Justify your answer.

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Q: Show whether or not F is a conservative field. If it is, find a potential function for it and use it…

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Q: b) Show the force field M UTM UTM F(r, y, z) = (r²y + In(yz)) i+ UTM 3 + y cos(2z) ) j+ tial…

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Q: If F (x, y) = x2 i + y2 j is a conservative vector field, find its potential function. With the…

A: The solution are next step is

Q: 7. Determine if the given vector field F is conservative on some domain and, if it is, find the…

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Q: (a) Suppose a vector field F(x, y) construct a potential function o(x, y). i+ is conservative. Then

A: Consider the given vector field.

Q: How do you determine whether a vector field in ℝ2 is conservative(has a potential function w such…

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Q: 5. Is the following vector field F(r, y) = (2x – y, -x + 3y?) conservative? If so, find a potential…

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

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Q: Determine if the vector field F(x,y)= (x+y,x−y) is conservative? If it is, find its potential.

A: Given Data The vector field is: F(x,y)=(x+y,x-y).   Write the vector field in standard form, The…

Q: For a force field F, if curl F= 0, then the field is nonconservative field. True False

A: False

Q: Determine whether F(x, y) = xi +9yj is a conservative vector field. If so, find a potential function…

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Q: 3. Use the fact that F = is a conservative vector field to evaluate SF. dr when C is the path r(t)…

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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: Compute the line integral of the vector field F = (3zy1, 4z, -y) over the path c(t) = (e*, e', t)…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(4x + y + 62) . F(1, y, 2) =

A: we have to find the gradient vector field of f

Q: 2. Given that F(x, y, z) = (e, xey + e², ye²) is a conservative vector field. a. Find a potential…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

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

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Q: Let f(x, y, z) = 3xyz + y?z. Find the gradient field Vf.

A: Formulae of gradient field is given below

Q: Find a potential function for the conservative vector field. F(x, y) = xex*4Y(2yi + xj)

A: If curl f is zero then conservative field

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: Find div ccurl F) = v(♡XFJ For the V cetor Field given By F(AoyoZ)= X=i -6xzj + yz K

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

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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: Evaluate both sides for the field- rectangular parallelepiped X = 0 and 1 Y=0 and 2 and Z=0 and 3.…

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Q: If F is a conservative vector field on a region R, how do you evaluate∫C F ⋅ dr, where C is a path…

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Q: Find a potential function for the vector field F by inspection. F = (4x, 4y) Ф(х, у) 3

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Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: 10. Use the Divergence Theorem and the vector field F = to compute the outward flux from the region…

A: Here we will evaluate the outward flux.

Q: 1. Is the vector field V (x, y, z) = (2ry, x² – 2², –2yz) conservative?

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: i) Show that F is a conservative vector field.

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

A: Given: The conservative field F, F=y+zi⏜+xj⏜+xk⏜; P10,0,0, P29,10,18 To find: Work done by force…

Q: 6. Show that F = [y? cos x + z3, 2y sin x – 4, 3xz2 + 2] is a conservative force field. Find the…

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Q: Which of the following functions is a potential function for the conservative vector field F (x, y,…

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Q: Which of the following functions is a potential function for the conservative vector field F (x, y,…

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Q: 3. Show that the vector field F = -C with C> 0, is conservative and find its potential.

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Q: Show that the vector field F(x, y)= (12x² +3y² +5y)i+(6xy– 3y² +5.x)j is a conservative vector field…

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Q: Which of the following functions is a potential function for the conservative vector field F(x, y,…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?

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Q: (a) Suppose that you are asked to determine the path that requires the least work for a force field…

A: For Conservative Force Field  amount of work it takes to move a particle from one point to another…

Q: Show that the vector field F(x,y,z)=yz^2i+xz^2j+2xyzk is conservative, find a potential function f,…

A: The given vector function is F(x,y,z)=yz2i+xz2j+2xyzk The given vector field F is conservative if…

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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