A particle moves along the line segments from the origin to the points (2, 0, 0). (2, 4, 3). (0, 4, 3) , 3 The motion is Y. and back to the origin. Note that this (counterclockwise) path is a rectangle on the plane Z = under the influence of the force field F = z'i + 2xyj + 4yʻk. Use Stokes' Theorem to find the work done.

Q: A force F = -3i +j+6k acts through the point (5,-2,-1). Find its moment about the point (3,0,2).

A: Moment of force about the point is given by cross product of position vector r about a point and…

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Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder + (y − 1)² = 1 (a)…

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Q: Find a unit vector u that is normal to the level curve of f(x, y) = 5x²y through P = (x, y) = (1,-4)…

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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: Let the temperature T in degrees at the point (x,y,z), with distances measured in cm, be T(x,y,z)=3x…

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

Q: a) The position of point moving in space is given by R(t) = 3 tan t i + cott j +2 lnt k, find the…

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Q: f(x, y, z) = sin(ry + z) foksiyonunun| P(1, 7/4, 7/2) noktasinda v = -2i + j+ 2k

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Q: Q1] Find a unit vector normal to the surface 3x2 у — узz? аt the point (1,-2, -1)

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Q: What is the principal unit normal vector for the curve: r(t) = (3t + 1)i + e'j .at the point P = (1,…

A: Let r(t) be the curve, then the unit tangent to the curve is given by T(t)= r'(t) / |r'(t)|. The…

Q: Let the velocity vector be v(t) = (6 cos(3t), 8 exp(2t), 3t2). Compute the acceleration vector a(t).

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Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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Q: The acceleration of a particle at any time >=0 is given by: dr a = == (25cos2t)i + (16sen2t)j +…

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Q: Consider the function f(x,y) = ex cos y + e³ sinx and the points P(1,0) and Q(-3,3). Find Duf at the…

A: The given function is fx,y=excosy+eysinx and the points are P(1,0), Q(-3,3). The objective is to…

Q: A particle is acted upon by constant forces 4i+j-3k and 3i+j-k and is displaced from the point…

A: Introduction: When a force is acting upon a particle and there is a displacement, the force works on…

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

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Q: 5. For f(x, y) 2x +y v 3i-4j find the rate of change of fat (1,2,6) in the direction of the vector =…

A: rate of change of the function at the given point along the given direction

Q: An airplane took off from point (3, 0, 0) at an initial velocity, v(0)= 3j with an acceleration…

A: Let r(t) be a position vector of a particle at time t. Then the velocity vector  v(t)=ddtr(t) Also…

Q: Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N is a vector…

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Q: Compute the work done by the force F = (sin(x + y), xy, x²z) in moving an object along the…

A: Given information:Force vector in Newtons.Initial point .Intermediate point .Final point .To find:…

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

A: Given that, gu,v=u2e-v,8,0 and v=3i+4j. Find the value of ∂g∂u and ∂g∂v at the point (8,0).…

Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

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