Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi + xzj + xyk C: line from (0, 0, 0) to (7, 5, 4) 168 X 10 5 36 10 5 5 10

Q: = f(x,y) = e²+y. For a unit vector u in R?, it is fü(0, 0) = 1. Let z true that

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Q: Find work done by the force field f = (XY, 2, 42) when a Particle moves along the straight line from…

A: The force field is given as,find work done by the force field F when a particle moves along the…

Q: The given vector function is F(x, y, z) = (2x – y + In(z² + 1))î + (x – 6e²y + 4 cos 4y)ĵ + | 2xz -…

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Q: 3. A velocity field v= ui + vj + wk is given as: u=x+2y+3z+ 4t², v = xyz +t and w = (x+ y)z + 21.…

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Q: Determine which of the following forces are conservative. If a force is conservative, find its…

A: Let us consider the force F→ The curl of the F is obtained as curl F=ijk∂∂x∂∂y∂∂zFxFyFz If F is a…

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 that the acceleration vector is a(t) = (e²t + 2t, e²t – 3,0) and also that the velocity…

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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: 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: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0…

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Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0…

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Q: F.dr for F(x, y, z)=(x²)i+(x²y)j-(y²z)k where C is given by the vector 1. Evaluate Fa C function…

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

A: In the given problem, force is given and the displacement straight line is given. We have to find…

Q: 3. A velocity field v= ui + vj + wk is given as: u = x+2y+3z + 4r°,v= xyz +1 and w = (x+y)z + 21.…

A: u=x+2y+3z+4t2 a1 = ∂u∂t+u∂u∂x     =8t +u    = 16+22    =38 v=xyz+t a2=∂v∂t+v∂v∂y =1+vxz =1+3 =4

Q: 2. [14 points] Find the work done of the force field F(r, y, z) the trajectory r(t) = (t,t2, t³)…

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Q: 4. A force F = (0+ 1)i - 0j – R Determine the vector moment, M, of F about the point P with the…

A: We have to solve given problem:

Q: Q1. Find the vector function r(t) given that r(0)= i+2j. and r'(t)= (2et, 3t², 4 cost)

A: The given data is: r0=i+2jr't=2et, 3t2, 4cost Find the vector function rt