Find the work dr done by the force field F = (y,x,z) on a particle that moves along the line segment from (1,-3,2) to (12, 14, 18). Round your answer to 3 decimal places.

Q: Calculate the work done by a particle moving under the influence of a force F = -(2z + y)ê + x²yŷ +…

A: The general form of a vector-valued function in three dimensions is given by F=F1x^+F2y^+F3z^…

Q: Consider the force field F = (2xzez — 4, cos³ z, x²eª²z – 3y cos² z sin z Find the work done by F in…

A: Given: The force field is F→=2xzex2z-4,cos3z,x2ex2z-3ycos2zsinz and the given given curve is…

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: Find the gradient vector field of f(x, y, z) = 9x5 + 7y3 + 6z?

A: To find the gradient of  f(x,y,z)=9x⁵+7y³+6z²

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: 10. Compute the work done by the force F(x, y) = (x²–y) i+xj acting on an insect as it moves along a…

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Q: Find the work done by the force field F(x, y) =(2y'+2xy, 6xy+x +1) in moving a particle over the…

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Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

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 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: Q3) Compute the work done by the force field F(x,y,z) = (3x, xz, y) on the curve C, where C is the…

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Q: Without using a potential function, find the total work performed by the force field F(x, y) = = (2x…

A: Given the vector field F→x,y=2xsiny+y2ex,x2cosy+2yex. The particle moves along the curve x=sinπy2…

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: 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 in moving a particle along the curve C. F(x, y) = (x - y°)i+…

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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: 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 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 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: The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to $(r) : equi-…

A: The formula to calculate the vector which is normal to the equipotential  line of the potential…

Q: Find the work done by the force field F(x, y, z) = on particle that moves along the line segment…

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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: A particle starts at the point (-2, 0), moves along the x-axis to (2, 0), and then along the…

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Q: Find the work done by the force field F(x, y, z) = (x – y², y – z?, z – x2) on a particle that moves…

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Q: Exercise (3): Find the work done under the influence of the force F = 3xyi – 5zj + 10xk along the…

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Q: Find the work done by the force field F(x, y) = (x^2-lny)i + (e^x^2+y^2)j on a particle that travels…

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Q: The work done by a force field in a moving particle around a closed path is zero.

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Q: Compute the work done by the force along the curve (use defini- tion): 1 F = [3r – y + y] curve is…

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Q: Find the work done by the force field F(x, y, z) = (x − y², y - z², z - x²) on a particle that moves…

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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: 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: Show that the work done by a constant force field F = a i + b j + c k in moving a particle along any…

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Q: Confirm that the force field F(x, y) = yeyi+ xey j is conservative in some open connected region…

A: We have to find the work.

Q: Find the work done by the force field F(x, y) = x sin y1 + y J on a particle that moves along the…

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Q: Find the work done by the force field F(x, y) = x 2 i yex  on a particle that moves along the…

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Q: Without using a potential function, find the total work performed by the force field F(x,y) = (2xsin…

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Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

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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: Find the work done in moving a particle in the force field F = (2r + y)i + (3y – 2)j along the…

A: Work done in moving a particle in the force field along along the curve C is:  ∫CF→·dr→ here F→ is…

Q: Without using a potential function, find the total work performed by the force field F(x, y) =…

A: Work done by vector field while moving a particle along a curve = Line integral of that vector field…

Q: Exercise (3): Find the work done under the influence of the force F = 3xyi – 5zj + 10xk along the…

A: The work done by a force on displacing a object by a certain distance is given by dot product of…

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: 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: 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(z,y,2) = Ir+v,rs, y+:) on a particle that moves along the…

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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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Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: