ind 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, o) to (9, 7, 6) 10 5 10 10 y 5.

Q: OSketch the vector field F(x, y) = -5i – 5j and calculate the line integral of F along the line…

A: Solution:-     Given that, F→ x,y=-5i∧-5j∧we have to calculate the line integral ∴we have to…

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: Find the directional derivative of the function at the given point in the direction of vector v.…

A: the vector field is  g(x,y,z)=(x+4y+3z)32  point (2,1,1) to find the directional derivative in the…

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: If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. Find…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Find the component of the force 5i+7j-k in the direction of the displacement PQ, where P(3,0,1) and…

A: The given force is

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: For vector field F = (-2y, y), y > 0. Find all points P such that the amount of fluid flowing into P…

A: The vector field given is as follows: Fx, y=-2y, y We are asked to find points P=x, y such that the…

Q: Let F(x, y) = (4x², 3y2). Compute the flux F nds of F across the boundary of the triangle with…

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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: 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: