Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…
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Q: Find the flux of the vector field F(x, y, z) = 3xi+3yj+6zk across the portion of the surface z = 25…
A: The flux F across the surface is given by ϕ=∫σF·nds=∬RF·∇GdA
Q: 4. Find the work done by the force field F (x,y) = (x + y)î + (xy)ĵ in moving a particle along the…
A: The force field is given by F→ = x+yi^+xyj^ The end points of the straight line along which the…
Q: Find the work done by the force F = 9xy i + 6yj acting along the piecewise-smooth curve consisting…
A: Given that F=9xy i+6y2 j Let r=xi+yj+zk ⇒dr=dx i+dy j+dz k Now, F.dr=(9xy i+6y2 j+0k)(dx i+dy j+dz…
Q: Find the workdone in moving a particle in a force field given by f=3xyi-5zj+10xk along the curve…
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Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…
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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…
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Q: Compute the work done by the vector field F(x, y, z) = (,2, 2yz) when moving a particle: 1+? > a)…
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Q: Use the Green's theorem to find the work done by a force F(x, y) = on a particle that moves…
A: find explanation below
Q: A particle starts at the point (-1, 0), moves along the x-axis to (1, 0), and then along the…
A: Consider the provided information, The work done by force F in moving particle along the path C is…
Q: Find the flux through through the boundary of the rectangle 0 < x < 6, 0 < y < 5 for fluid flowing…
A: Given F→=x5+y , y cos3x flux=∫cF→.n^ ds =∫∫Ddiv F dA
Q: Let divF(x,y, z) = 4x³ + 4y³ + 42³ , where F represents the flow of a vector field. Estimate the…
A: Concept Used:- Divergence Theorem Flux=∫∫∫∇.F dVwhere ∇.F is the divergence of FVolume of the…
Q: Find the work that is done by the force F = (x + y)î + xyj – z?k acting on a particle that moves…
A: Convert function into parametric function. Then find work done by doing line integration.
Q: A particle moves along line segments from the origin to the points (1,0,0), (1, 2, 1), (0, 2, 1) and…
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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…
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Q: A particle moves along line segments from the origin to the points (1, 0, 0), (1, 5, 1), (0, 5, 1),…
A: Obtain the equation of the plane passing through the 4 points (1,0,0), (1,5,1), (0,5,1) and the…
Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…
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Q: Find the flux of the vector field F = (x, z, - y) through the helicoid with parameterization r(u, v)…
A: Given :- The flux of the vector field F→ = x3 , z , -y through the helicoid with the…
Q: Find the flux of the vector field F = (y, - z, x) across the part of the plane z = 4+ 2x + 3y above…
A: The given vector field is, F→=y, -z, x. The given part of the plane is z=4+2x+3y And the rectangle…
Q: A particle moves along line segments from the origin to the points (1, 0, 0), (1, 5, 1), (0, 5, 1),…
A: First obtain the equation of the plane passing through the 4 points (1,0,0), (1,5,1), (0,5,1) and…
Q: Find the work done by the force field F(x, y, z) = y + z, x + z, x + y on a particle that moves…
A: Given that the force field,
Q: Determine the work done by the force field F(x, y, z) = (x − y2, y −z2 , z − x2) on a particle that…
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Q: How much work is required to move an object in vector force field F = (yz, xy, xz) along path r (t)…
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Q: Calculate the work done by the force F(x, y) = y?î+ xyj in moving a particle along the line which…
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Q: Find the work done by the force field F(x, y, z) = (y + z, x + z, x + y) on a particle that moves…
A: It is known that
Q: Compute the work done by the force field F(r, y) = (2, 3r) acting on an object as it moves along the…
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Q: The motion of a liquid in a cylindrical container of radius 2 is described by the velocity field…
A: Given,F(x,y,z) = -19y3i + 19x3j + 7k⇒curl F = ijk∂∂x∂∂y∂∂z-19y319x37 = 0i + 0j +…
Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).
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Q: Find work done by a force field F= in moving object along the line segment from the point (2,1,3) to…
A: Given, F=1y-x,xyz,ex2+y2+z2
Q: The work done by a force field in a moving particle around a closed path is zero.
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Q: 2的 在年
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Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…
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Q: Compute the flux of the vector fields F(x,y, z) = (, y, z) across the 1 and z = 4 whose vertical…
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Q: Without using a potential function, find the total work performed by the force field F(x, y) =…
A: The work done by the path E is given by, W=∫EF.dr If the force vector is: F(x,y)=<2xsiny+y2ex,…
Q: Let divF(x, y, z) = 4x³ + 4y3 +4z³, where F represents the flow of a vector field. Estimate the flux…
A: Given divF→x,y,z=4x3+4y3+4z3radius r=0.1 Centered at point 1,1,1
Q: Find the work done by the force field F(x, y, z) = (y + z, x + z, x + y) on a particle that moves…
A: Given To find the work done by the force field Fx,y,z=(y+z,x+z,x+y) on a particle that moves along…
Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…
A: Given: f(x, y, z) = 9x2 − xy − z2
Q: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…
A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…
Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…
A: Given : f(x,y,z)=9x2y+5z2 To Find : Conservative Vector field by finding it's gradient
Q: Use Stoke's Theorem to find the work done by the force field F(x, y, 2) = (ein + 2y?, 6x + tan- y,…
A: Given : force field F→x, y, z=esinx+2y2, 6x+tan-1y, xz To find : work done by the force…
Q: Without using a potential function, find the total work performed by the force field F(x, y) = (2x…
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Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) = z sin(ry). F(2, y, z) = (
A: Given function is f(x,y,z) = z^2 sin(xy)
Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y,…
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Q: Let divF(x, y, z) 4x3 + 4y3 + 4z³ , where F represents the flow of a vector field. Estimate the flux…
A: Given that a small sphere of radius 0.1, centered at the point (1, 1, 1).And div F…
Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (esin x + 2y², 6x + tan-…
A: We have to find the work done by the force field F→x,y,z=esinx+2y2,6x+tan-1y,xz in moving a particle…
Q: A hot air balloon is shaped like a truncated sphere like the figure. The gases escape through the…
A: Given a hot air balloon has a truncated spherical shape. The velocity vector field Vx,y,z=∇×Fx,y,z…
Q: Find the work dr done by the force field F = (y,x,z) on a particle that moves along the line segment…
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Q: Use Green Theorem to find the work done by the force field, F(x, y) = (e* + x²y,e – 2xy) in moving a…
A: According to Green's Theorem ∫CPdx+Qdy=∬D(∂Q∂x−∂P∂y)dA where F→ = ⟨P, Q⟩
Q: Find the work done by the force field F(x, y, z) = (x – y², y – z², z – x2) on a particle that moves…
A: We have to find the work done by the force field F(x,y,z)=<x-y2, y-z2, z-x2> on a particle…
Q: Find the work done by the force F(x, y, z) = (x, —z, 2y) in moving straight from (0,0,0) to (1,1,0),…
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