d the work done by the force field F in moving a particle along the curve C. F = xyi + 3j + 9xk; C:x = cos 6t, y = sin 6t, z = t, 0 sts- 12

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+e'cos (y)) j through the right…

A: Given vector field is F=  x2y + ex siny  i + x2 + ex cosy j Curve r2=cos2θ

Q: Find the work done by the force F = zi + xj+ yk in moving a particle along the curve x = t y = t²…

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Q: Find the work done by the force field F(x,y)= x2i - xy j in movinga particle along the…

A: Consider the following field:

Q: If C is the curve given by r (t) = (1+2 sint)i+ (1+ 2 sin? t)j+ (1+1 sin' t) k, 0<t< and F is the…

A: Given:

Q: 1. Find the work done by the force field, a. F(x, y) = x²i – xyj in moving a particle along the…

A:

Q: 10) Find the potential function for the vector field F=-i-4j - k. z² Then compute the path integral…

A:

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…

A:

Q: Find the work done by the force field F(x, y, z) = 2xi+ 2yj+7k on a particle that moves along the…

A: “Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: Given the force field F, find the work required to move an object on the given orientated curve. F =…

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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) = xi +…

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Q: 9. Find the work done by the force F(x, y, z) = e³i + ln(x)j + 3zk, in moving an object over the…

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Q: 5. Find the potential function for given vector field: F = (e* In(y))i + + sin(2))j + ycos(z)k

A:

Q: 6: Find the work done by the force F = -7y i+ 10x j along one loop of the curver = sin 70 (in the…

A: Given

Q: Consider the force field F (ev – e2", (x + )e") and the curve C = C1 U C2 where C1 is the line…

A: Given : force field F→=ey-e2x, x+12ey and the curve C=C1∪C2 where C1 is the line segment from 0, 0…

Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzĵ + xyk in moving from (1,1,1) to…

A: The equation of a line joining by the points and is given as the following.

Q: 4. Find the work done by the force field F = (x? sin(y),y) on a particle that moves along the cubic…

A: Given: The force field, F→=x2siny,y on a particle that moves along the cubic y=x3 from 1,1 to 2,8.

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

A: Formula: The work done by the force field F that moves along the curve C is: W=∫C F·dr Suppose the…

Q: | 23. Find the outward flux of the field F = ( 3xy i + (e* + tan¯ly)j х 1 + y?, across the cardioid…

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Q: Find the work done under the influence of the force E = 3xyi – 5zj + 10xk along the curve x= t² + 1,…

A:

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

A: Step2

Q: 23. Find the outward flux of the field i + (e + tan'y)j 1 + y², F 3xy %3D across the cardioid r =…

A: Given: The following formula is used to find the outward flux, Comparing with the general form,…

Q: Find the work done by the following force field F(x, y) = 3(v+ 2)'0i + 30x (v + 2)°j %3D in moving…

A: The work done is a scalar quantity, which is equal to the dot product of force applied to the body…

Q: If r(t) = cos(2t)i + sin(2t)j – 4tk, compute the tangential and normal components of the…

A: Given:- rt=cos2ti+sin2tj-4tk Find Tangential and normal component of acceleration vector

Q: ii) Evaluate the vector line integral of F, F. ds, where y is an oriented curve defined as follows:…

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Q: Given the force field F = (2xze*z – 4, cos³z, x²e**z – 3ycos²z sin z) Solve for the work done by F…

A:

Q: Find the work done by force F(x, y) = 4yi + 7xj + (x + y)k in moving an object along curve r(t) =…

A: To find the workdone along the given path

Q: Q1 (a) Given the force field F = (z3 cos x + 2xy²)i + (2x²y – 2)j + (3z² sin x - 4)k (i) Prove that…

A:

Q: (iv) Find the work done by the force field F(x, y) = x²i+ yeªj on a particle that moves along the…

A:

Q: Find the work done by force field F on an object moving along the indicated path. F(x, y, z) = xi +…

A: To solve the following problem

Q: Identify the work done, J. F.dr by an electric field, E = (x + xy)î + (y + 5)f – 5zk V/m to move an…

A: Work done along the curve C by vector field F . Where C is given by parametric equation r(t)…

Q: Find the work done by the force field F(x, y) = (3x² + y²) i+ (2y²)j along the curve C given by ř(t)…

A: The given vector field is  f→x,y=3x2+y2i→+2y2j→       (1)  and the curve is  r→t=ti→+e2tj→…

Q: I Need help for this question

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Q: 4. Evaluate the line integral Vf-r'dt, where the curve C is given by the vector function r(1)…

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Q: Consider the force field F = (2rze"*: – 4, cos' z, r²e*** – 3y cos? z sin z - Find the work done by…

A:

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+ e*cos(y))j through the right…

A: Solution

Q: The work done in moving a particle in the force field F= x- i+ 3xy j from (0,0) to (1,2) along the…

A:

Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzj + xyk in moving from || (1,1,1) to…

A: The given question is related with work done. We have to find the work done ∫CF→ . dr  in the force…

Q: (iv) Find the work done by the force field F(x, y) = x²i+ye¹j on a particle that moves along the…

A: We have to find the work done by the force using line integral

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: Find the work done by force F(x, y) = 2yi + 3xj + (x + y)k in moving an object along curve r(t) =…

A:

Q: b) Show that the force field F(r, y, z) = 3x zi+ 2y ln z j+ is independent of path and find its…

A: F(x,y,z)=3x2zi +2ylnzj+(y2/z +x3)k r(t) =ti +tj+t2k F(t ) =3t4i +4tlnt j +(1+t3)k dr = dt i +dt j…

Q: Calculate the work done by F(x,y) = ⟨2x + ln( 2y2 −1), arctan(y4 +2y +1) + 4xy / (2y2 − 1⟩ along the…

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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) = xi +…

A:

Q: Find the work done by the force field F = x i + y j + z k in moving an object along the curve C…

A: Given Force - F = xi+yj+zk                .................................(1)Position vector - r(t)…

Q: (b) A particle moves once around the circular path with radius of 1. Using Greens' Theorem, compute…

A: see below the answer

Q: 1. Calculate the work done when a force F = 3xyî – y?j moves a particle in the xy-plane from (0,0)…

A: Take dot product along limit of integration and integrate

Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

A:

Q: Given the force field F, find the work required to move an object on the given orientated curve. F=…

A: Let F=Pi^+Qj^ ∂Q∂x=∂P∂y=1 The force field is conservative.

Q: Given the force field F = (2xze* - 4, cos°z, x?e**: - 3ycos?z sin z) Solve for the work done by F in…

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Q: Calculate the flux of the field F across the closed plane curve C where F= xi+ vj and the curve is…

A: