Show that the work done by a constant force field F = a i + b j + c k in moving a particle along any path from A to B is W = F.vectorAB

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: Show that work performed by a constant force field F over any path C ~ from P to Q is equal to F •…

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Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (ein z + 2y², 6x + tan¬1…

A: Given force field is F→(x,y,z)=esinx+2y2, 6x+tan-1y, xz Now, we will find the Curl(F→).…

Q: Confirm that the force field F(, y) = 2xy°i+ 3x²y² j is conservative in some open connected region…

A: Solution:- The given function is  F(x,y)=2xy3i+3x2y2jpoint P(-9,8) and Q(6,7)we have to find the…

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: 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: 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: Compute the work done by the force field F = in moving a particle along the line segment from (1, 1)…

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Q: Let F(x, y) = ye*Yi + xe*j Show that F is a conservative vector field on the entire xy -plane. Find…

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Q: Compute the work done by the vector field F = in moving a particle along the circle x? + y 1 from…

A: Please see the answer below

Q: Find the work done by the vector field f = to move a particle along the arc of the hyperbola y=1/x…

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Q: Determine whether the vector field F(x,y,z)=(y,x,1) is conservative on R° . If so, determine a…

A: Given the vector field Fx,y,z=y,x,1=yi→+xj→+k→.

Q: Compute the work done by the vector field F = in moving a particle along the circle x + y = 1 from…

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Q: A pasticle depicts ts motion in Such a ulay at time ť is P=xîty where, 2= acoskt and y=bsinkt. that…

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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: Compute the work done by the vector field F = in moving a particle along the circle x + y = 1 from…

A: Solution is given below

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: Find the work done by the force field

A: Given: The given function is, With A(1,1) and B(4,4). To find: The work done by the force field F…

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

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Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x Y F(x, y) =

A: To find the work done by the force field F in moving an object from P-3, 7 to Q7, 5. Fx,…

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: 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: 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: Integrate the vector field h (x, y, =)=ry i+yz j+x k over r (1u) = ui+ j+k, -ןue-L1

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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 the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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Q: Find the work done by the force field F(x,y) = (-y,x) in moving an object along the path y = V4 – x2…

A: Given force field Fx,y=−y,x and object moving along the path y=4−x2  from 2,0 to -2,0. We have to…

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: 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: Calculate the work done in moving a particle in the force field F = 3x2î+ (2xz-y)ĵ+ z k along a…

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Q: 6. What is the corresponding vector fieldV for the scalar potential p(x, y)= In(x+ ¥)?

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Q: Find potential 9, for the conservati ve field the vector F (x, y,a)- (2xe? - y*sinx) î * sinx) î +…

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Q: Is the vector field F = [yze"yz, xze#yz, xye"yz] conservative? %3D O Yes O No

A: The vector field is conservative if ∇×F→=0 therefore, find ∇×F→ ∇×F→=ijk∂∂x∂∂y∂∂zyzexyzxzexyzxyexyz

Q: Use Green's theorem to find the work done by the force field F(x.y) %3D хyi + 1 x²+xy]j on a…

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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: 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: Find the work done by the force field F in moving an object from P(-4, 8) to Q(6, 4). F(x,y) = 2* 1…

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Q: The outward flux of the vector field F=(x,0, z) across the cylinder x + y = 1, for 0<z<1, is %3D…

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Q: Compute the flux of the vector field F(x,y,z)=5xj+2yk→through the surface S, where S is the part of…

A: Flux problem...

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: Find the work done by the force field F in moving an object from P(-9, 5) to Q(3, 5). F (r, y)

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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) = x²yi + y²j around the circle with radius 2.

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