2. Given vector field F= (-2y, z-2x, y + z), find the work done by ♬ on a particle that moves along a the straight line from (0,1,0) to (0,2,5). 20

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: Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the…

A: v→=y2i→+1.3x2j→ Initial point 1,2 ∆t=0.1

Q: If r(t) = u(t) x v(t), where u and v are the vector functions given below, find r'(2). u(2) = (6, 3,…

A: To find r'(2).

Q: C

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Q: Suppose f(x, y) = (a) ▼ f(x, y) = (b) ▼ f(-0.7, 7) = tan(x) + y and u is the unit vector in the…

A: Given that f(x,y)=tan(x)+y  and u is the unit vector in the direction of <2,3>now, ∇f(x,y)=fx,…

Q: Find the electric flux PE across the part of the cylinder x² + y² = 9,0 ≤ z ≤ 2, in the direction of…

A: Given information:The electric field is given as .The surface is a part of the cylinder defined by…

Q: Suppose a particle, whose initial position is (1, 0, 0), moves with velocity given by v(t) = (-1,…

A:

Q: 2y X in the direction of (1, 2). Then, Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ ƒ(6, π) = = = sin (c)…

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Q: 10. Find r'(1) given the following vector function. 2 3t j+ A) rf)=--i-9² j+ r'(t) : 4 -i-9t? B)…

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Q: Compute fa(P) where is a unit vector in the direction of . a) f(x, y) = x² + 2xy + 3y², P = (2,1), v…

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Q: Find the work done by F over the curve in the direction of increasing t. F = 4zi + 4xj + 4yk, r(t) =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: For the vector-valued function r(t) = t³i + (2t² + 1)j + (3t − 6)k find the following and express…

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: Suppose the vector field v(x, y, z) = (4xy2, -4xz², 5x) represents the velocity field of a fluid.…

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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: A particle passes through the point P=(−2,−1,2) at time t=7, moving with constant velocity…

A: To find the position vector of the particle at time t.

Q: (c) Calculate the divergence (V.Ä = div Ã) and curl (V × Ā = rot Á). of the following vector fields.…

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Q: Prove that (Y - Y1)'(Y - Y1)= (-Y1)'(- Y1) + (Y-P)'(Y-P) where Y = n 1 Y and 1 is an n-dimensional…

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Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Sex. (x+y)ds where C is the straight-line segment x = 3t, y = (3-3t), z = 0 from C (0,3,0) to…

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Q: 2 Locate the numbers z₁+z₂ and z, - z₂ vectorially when z₁ = 2i, z₂ ==-i. 3

A: Use addition the evaluate these numbers then plot it

Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt, n' = dxn, b' = d xb and…

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Q: Find two different vector parametrizations of the line through P = (8,8, 4) with the direction…

A: A line through  with the direction vector .To Find:Vector parametrization of the line.