field F = (z³cos x + 2xy2)i + (2x²y – 5)j + (a) Given (3z2 sin x – 2)k the force (i) Prove that F is conservative (ii) (iii) By using formula VØ = F, find a scalar potential Ø for F. Hence, compute the amount of work done against the force field F in moving an object from the point (0, -1, 1) to (1, 2, 2).

Q: 5) Consider the conservative force field F(x, y) = (6x²y? + cos(x), 4x y). a) Give a general…

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Q: 6. Let F = (2xy)i + (x²)j be the force field (a) Show that F is conservative. (b) Find the potential…

A: Oi

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Q: 1- Prove that the force field F known as : Prove that the force field defined by F = (y*z' -6xz? )i…

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Q: 5. Find the work done by a force F = [x2,y², z²] acting on a particle moving along the curve x = cos…

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Q: = (2xy + z³)i+x²3+3xz²k is conservative force field. Find the scalar potential Show that F = of F.

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Q: 3. Use Green's theorem to find the work done by the force field F(x,y) = xyi + (;x² + yy)j on a…

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Q: 6. Use Green's Theorem to find the work done by the force field F = ( 2xy, x² + x ) on a particle…

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Q: 1. Consider, F(x, y) = 2e2*siny i + e2*cosy j Show that F is a conservative vector field on the…

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Q: Find the outward flux of the field F = 2xyi + 8yzj + 6xzk across the surface of the cube cut from…

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Q: (b) Given the force field F(x, y, z) = (z³ – 2xy)i – x²j + 3xz² k (i) Show that F is a conservative…

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Q: Find the work done by the force field F(x,y) = 4yi + 2xj in moving a particle along acirclex^2 + y^2…

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Q: b) Given the vector field OU F(x, y, z) = 3z cos x i+ x ln y j +e° tan a k. Determine i. div F, ii.…

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Q: 16. Find the work done by the force field F(x, y, z) = (x – y²)i+ (y – 2²)j+(z – x²)k on a particle…

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Q: F - () (3x²y²z and F = 2r³yz Q.)11.1 Be (a) Explain why vector fields are conservative. (b)…

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Q: A particle starts at the point  (−4, 0),  moves along the x-axis to (4, 0), and then along the…

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Q: ) Let F(x, y) = (3x² + y²)i + 2xyj. (a) Test if F is a conservative vector field. (b) If F is…

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Q: I Need help for this question

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Q: 2. For the vector field given by: F(x, y) = (2x + e¬* cos y) i + (y² + e=* sin y) j a. Show that the…

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Q: a) Find the values of a,b,c which make f(x,y,z) = sin (xªy°z©) a potential function for the vector…

A: I have solved first part of your query. I request you to repost your query for next part

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Q: 1. Consider, F(x, y) = 2e2*siny i + e2*cosy j %3D i) Show that F is a conservative vector field on…

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Q: 5. Find a potential function corresponding to the vector field F(x, y, z) = (2x, 3Y, 4z).

A: