5. Is the following vector field F(r, y) = (2x – y, -x + 3y?) conservative? If so, find a potential function.

Q: How do you graph the vector field F = ⟨ƒ(x, y), g(x, y)⟩?

A: Given: vector field

Q: If f(x, y) = x²y+ y² and F(r, y) = Vf(x, y), find Fo F(1, -2). %3D Select one: a. (-12, 0) b. (16,…

A: We have given multiple choice question each having one option correct based on the function gradient…

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: Sketch the gradient vector field for the funtion f(x, y) = xy.

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Q: Is the vector field F(x, y) = (In y + sin(e²“), #

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Q: Evaluate the integral curves for the vector field F(x,y) : i – 4xy²j . О a. - 4у — х2 = C 4x2y2 Ob.…

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Q: Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %3D

A: In this question, we find the flux of the vector field f(x,y,z)=xi The surface is a sphere of radius…

Q: Find the equation of the gradient vector field for the function f(x, y) = – læ² + 1y and then sketch…

A: The gradient vector field of given function is -2x i + 2y j

Q: What is the work done by a force field F (x, y) := 2x to move a particle in a straight line from (0,…

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Q: 1. Find the line integral in a vector field a curve consisting of 2 parts. First, the straight line…

A: Given F→=y,x+2y We have to find the ∫CF→⋅dr along the given path.

Q: Determine if the vector fields below are conservative. Find potential functions where possible. (a.)…

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Q: F - () (3x²y²z and F = 2r³yz Q.)11.1 Be (a) Explain why vector fields are conservative. (b)…

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Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

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Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):

Q: 6. What is the corresponding vector fieldV for the scalar potential p(x, y)= In(x+ ¥)?

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Q: Find the gradient vector field of f(x, y, z) = ln (xy² +sin yz³ - 5x^z)

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Q: A conservative vector field is given as F = 6xe'i + (3x²e" –10yz')j-15y²z°k. Find the potential…

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Q: The work done by the vector field F(x, y) = (-y², ²) along the arc of the parabola y = 2x² - 4x + 2…

A: According to question,Given Vector field,Fx, = -y2,x2Equation of pparabola,y = 2x2-4x+2

Q: 1) Sketch the vector field F. (i) F(r, y) = (ii) F(r,y, 2) = i

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Q: (a) Let F(r, y) = | flow line of the vector field. Show that c(t) = ( cos(t) + sin(t), – sin(t) +…

A: To find-  Let Fx, y = yx2 + y2, -xx2 + y2. Show that ct = 35cost + 45sint, -35sint + 45cost is the…

Q: Find the domain of the following vector functions:- (b) f(t) = Lnt- 1|i + e'j+ VEk

A: Given that , f(t) = ln(t-1) i +et j +t k To find :- Domain of f(t) Domain of f(t) is intersection of…

Q: 8. A particle follows a straight-line path from (1,2) to (5,7) within the vector field F(x, y) =…

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