Find the work done by force field F on an object moving along the indicated path. F(x, y, z) = xi + yj – 9zk, C: r(t) = 7 cos(t)i + 7 sin(t)j + tk, 0 st s 2n

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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: Find the work done by the force field F(x, y, z) = 4xi + 4yj + 6k on a particle that moves along the…

A: Explanation of the answer is as follows

Q: Find the work done by the force field F(x, y, z) = xyi+ yzj+xzk or a particle that moves along the…

A: Given: Fx,y,z=xyi+yzj+xzkr(t)=ti+t2j+t3k

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Q: Find the work done by the force field F = (y-x)i + (z- y?)j + (x - z)k along the curve r(t) = ti +…

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 6y3/2 i + 9xyj…

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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…

A: Step2

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…

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Q: Find the work done by the vector field F = ( – 2, – 4y, 2æ) in moving an object along C in the…

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Q: Find the work done by the force field F(x, y) = xi + (y + 7)j in moving an object along an arch of…

A: Given  Fx,y=xi+(y+7)j in the moving an object along an arch of the cycloid dr

Q: Find the work done by the force field F(x, y) = xi + (y + 7)j in moving an object along an arch of…

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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→…

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

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 2y3/2 i + 3x/ỹ j…

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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: Find the work done by the force field F in moving an object from A to B. F(x, y) %3D 2y3/2 i + 3x/у…

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Q: Find the work done by the force field F(x, y, z) = xy i+ yzj+xzk on a particle that moves along the…

A: Solution is given below:

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Find the potential function for the following vector field F(x, y, z) = (2x cos y – 2z3) î + (29+…

A: F = &lt;2xcosy-2z3, 29+2ye2-x2siny, y2e2-6xz&gt; To check F¯ is conservative  not we have t check…

Q: d the work done by the force field F in moving a particle along the curve C. F = xyi + 3j + 9xk; C:x…

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Q: Find the work done by the force field F(x, y) = y² i+ xyjin moving a particle along the curve r(t) =…

A: To find The work done by the force field in moving a particle along the curve.

Q: (а) Given the force field F = (z³ cos x + 2xy?)i+ (2x²y – 2)j + (3z² sin x – 4)k (i) Prove that F is…

A: Given force field is: F=z3cosx+2xy2i+2x2y−2j+3z2sinx−4k (i) To prove that F is conservative. (ii) To…

Q: Find the work done by the force field F(x,y,z)=4xi+4yj+5k on a particle that moves along the helix…

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Q: Find the work done by the force field F(x, y, z) = 5xi+5yj+4k on a particle that moves along the…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Find the work done by the force field F(x, y) = (4 e* – y³ î + (2 cos(y) + x³ )j on a particle that…

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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…

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Q: Obtain the work done by the force field F(x, y, z)=xi - z³j+zek in moving a particle along a curve…

A: Given  Fx,y,z=xi-z3j+zeyk               =x,-z,zeyr(t)=sin ti+2etk                  0≤t≤π

Q: Find the work done by the force field F(x, y, z) = 4xi + 4yj + 3k on a particle that moves along the…

A: To find the work done by the below force field on a particle that moves along the helix r(t).

Q: Find the work done by the force field F(x, y, z) = 5xi + 5 yj + 7k on a particle that moves along…

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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: