Find the work done by the force F = x²yi– xy²j along the paths shown from (1, 1) to (4, 2). (4, 2) a (1, 1)

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: 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: 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: 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: 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: (c(2z+y), %3D ue of c in the joi F of W.

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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: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: Find the directional derivative of the field f(x, y, z) = In(4 x) at P = (1, –2, –5) in 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, z) = yzi…

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Q: Suppose you need to integrate the vector fieldv – (3 cos z, ef sin y)) along the curve parameterised…

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Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,- 2) to (2, - 4).

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Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

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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: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,-3) to (3,-9).

A: Given force is F→=xyi^+y-xj^ and straight line coordinates are 1,-3 and 3,-9

Q: 5. Suppose a particle is moving along a smooth path r(t) with constant speed. If a(t) + 0, show that…

A: Two vectors is perpendicular if their dot product is zero.

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: Show that the force F = (y^²2² - 6xz² ) ₁² + ²xyz²³ j^² + (3 xy² z ²-6x²²Z) k IS Conservative, hence…

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Q: Find the work done by the force F 6xy i + line segments from (-4, 4) to (0, 0) and from (0, 0) to…

A: Consider  F(x,y)=M(x,y)i+N(x,y)j is vector valued function then : if ∂M∂y=∂N∂x then F is called to…

Q: 5) Find the work done by the force field F(r, y, z) = ri-zj+y k in moving an object along the…

A: Work = Force X Displacement

Q: 6) Find the work done by the force field F(r, y, z) = ri+yjtzk in moving an object along the…

A: Work done = Force * displacement

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: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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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: 2. Prove that the directional derivative of f (x, y, z) = xy sin z at direction v = i+2j+ 2k is .…

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Q: Find the work done by the force F =xyi + (y - x)j over the straight line from (- 2, - 1) to (-1,0).

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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: Vector Field F = 6xi + (2y – y²)j+(6z – x³)k is Conservative Select one: True False

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Q: If an object moves along the line segment 'c' given by x = t, y = t?, t3 from P(0, 0, 0) to Q(2, 4,…

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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

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

Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

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: Find the directional derivative of the field f(x, y, z) = -4x³ + 3 xy² + 5 y³ at P = (-1,–3,5) in…

A: Given f(x,y,z)=-4x3+3xy2+5y3  we have to find directional derivative of f at P=-1,-3,5 in the…

Q: Find the work done by the force F (x; y) = xyi-(y-x)j over the straight line from (1,1) to (2,3)

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Q: Find the work done by the force F= xyi + (y - x)j over the straight line from (-1,- 2) to (2,1).

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Q: 4. Find the work done by the force F(r,y,2) = (x,-z,2y) in moving straight from (0,0,0) to (1.1.0),…

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Q: Find the Duf of f(x, y,z) = z In(x+ y) + e3y on the vector u = 3i -j-4k at Po(1,0,1)

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Q: Find the work done by the force F = 4xyỉ + (2x2 - 3xy)j by pushing a particle along the line segment…

A: Step:-1 Given Force is F→ =4xy i→ +2x2 -3xy j→ Here, given that particle moves along the line…

Q: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln zk moves along a path C where x = t2, y = t +…

A: The formula to find the work done by the vector function helps to find the required work done. The…

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: 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: Consider a beam of length 10m and negligible mass, modelled as a rigid body in the x-direction from…

A: Here I am attaching image so that you understand each and every step.

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

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Q: 3. A particle is located at a distance x meters from the origin, a force of x +2 newtoms is acting…

A: To find the work done

Q: Prove that the directional derivative of flay.2) = aysinz. direction v=i +2j+2k 1Is Sin Z at…

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Q: 2. Suppose that a function f: R3 → R³ defined by: f (х, у, 2) 3 (2х + Зу — z, sin(тхy?z-1),…

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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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