Find work done by a force field F=< zyz, e'+ > in moving object along the line segment from the point (2,1,3) to the point (1,-1,3).

Q: Find the work done by the force field F(x, y, =)=(: - =', y + 3:, = + x*) in moving a particle alon,…

A:

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

A:

Q: Find the work done by the force F = 9xy i + 6yj acting along the piecewise-smooth curve consisting…

A: Given that F=9xy i+6y2 j Let r=xi+yj+zk ⇒dr=dx i+dy j+dz k Now,  F.dr=(9xy i+6y2 j+0k)(dx i+dy j+dz…

Q: Find the workdone in moving a particle in a force field given by f=3xyi-5zj+10xk along the curve…

A:

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

A:

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 F = xyi + (y - x)j over the straight line from (1,- 2) to (2, - 4).

A:

Q: Sketch the vector field F(x, y) = xj, the line segment from (1, 4) to (7,4), and the line egment…

A:

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…

A:

Q: determine the magnitude of the force exerted by block Y on block X during this acceleration.

A: In this question, we need to find the force exerted by block Y on block X.

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: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…

A:

Q: A particle moves along line segments from the origin to the points (1, 0, 0), (1, 5, 1), (0, 5, 1),…

A: Obtain the equation of the plane passing through the 4 points (1,0,0), (1,5,1), (0,5,1) and the…

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

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: Determine the work done by the force F"(x,y,z)=(x²y,xy). to move a particle along the line segment…

A:

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 directional derivative of f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

Q: (True/False) Suppose the work done by a force F on a particle moving along a path C is given by x,…

A: True.

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

A:

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: Calculate the work done by the force F(x, y) = y?î+ xyj in moving a particle along the line which…

A:

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…

A:

Q: Q6/ A boxful has been moved a distance (2m) in a F = 5.2 i+ 3J horizontal direction due to effect of…

A: Work done by a force is equal to the product of Force applied in the direction of distance and…

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

A:

Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

A:

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: When body is an equilibrium ,the net force is vanish ulgn O İhi O

A: when body is an equilibrium the net force is vanish

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

A:

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: A particle moves along line segments from the origin to the points (2, 0, 0), (2, 4, 1), (0, 4, 1),…

A: Given Fx,y,z=z2i+5xyj+2y2k  Let r=xi+yj+zk⇒dr=dxi+dyj+dzk Now particle moves from origin O0,0,0 to…

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

A:

Q: A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of…

A:

Q: Find the work done by the force field F in moving an object from P(-9, 7) to Q(3, 3). 2.x. F (r, y)…

A:

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…

A:

Q: The force exerted by an electric charge at the origin on a charged particle at a point (r, Y, z)…

A: Given that  r=x,y,z is Position vector Force exerted by an electic charge at the origin F=Krr3…

Q: Sketch the vector field F(x, y) = xj, the line segment from (1, 9) to (6,9), and the line segment…

A:

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

A:

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

A:

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)

A:

Q: A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1),…

A:

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…

A:

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)=&lt;x-y2, y-z2, z-x2&gt; 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),…

A:

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: