Question 4 (a) Consider the scalar field f (x, y) = 3x² – 2y and the straight line segment from point P(3,6) to point Q(1, –1). (i) If C is the parameterization of the straight line segment from P to Q, find C. (ii) Find the work done by the force field f(x, y) in moving a particle from P to Q along curve C.

Q: Question 5 The closed path integral of the vector field F(x, y) = 2.r2 + y?' 2x? + y? along the…

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Q: 5. Find a potential function corresponding to the vector field F(r,y, 2) = (2r, 3y, 4:).

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Q: 1. Find the work done by the force field, a. F(x, y) = x²i – xyj in moving a particle along the…

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Q: 10) Find the potential function for the vector field F=-i-4j - k. z² Then compute the path integral…

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Q: QUESTION 4 a) Let F(x, y, z)=x²7+(cos y sin z) + (sin y cos z)k be a vector space. Show that F is a…

A: Here given that  F→x, y, z=x2i^+cosy sinzj^+siny coszk^ be a vector space. We have to show that F→…

Q: Question 3 Find the flux of the vector field F across the surface S in the indicated direction. F=…

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Q: Question 18 If F is a conservative vector field in R³ and C is a loop (curve whose initial and…

A: To find which thing is true about given line integral.

Q: Problem 48. Using the Divergence theorem to find the outward flux f s F- nds where the vector field…

A: Divergence theorem states that,

Q: Problem 4: For the vector field A=xz a- yz a,- xy a, verify the divergence theorem by computing (a)…

A: Gauss divergence theorem: If F is continuously differentiable vector filed over the volume V. Then…

Q: QUESTION 1 a) Evaluate the line integral F. dr in terms of a where F = cos yi + rj+ ye*k and C is…

A: Work done by the force is the line integral from initial point to terminal point. A force field will…

Q: Find the outward flux of the given field across the given cardioid. 5x i+ (e*+5 tan 1ly)j 1 + y2 F =…

A: The following formula from Green's theorem is used to find the outward flux, outwards flux=∮F·n…

Q: Problem 2. Let F be the vector field (xe² + cos(x), -ye², z sin(x)), and S the paraboloid 2 = 1- x2…

A: We will find out the required solution

Q: Problem 1. (Line Integration) Consider the curve c(t) = (e*, e-t) with 0 <t<1 and the vector field…

A: Given:

Q: Question 5 (C15.2) For the vector field function, F(x, y) — хі + уј and curve C: r (t) = (3t + 1) i…

A: Solution is given below:

Q: For Problems 2–3, you are given a vector field F and a curve C. Use the Fundamental Theorem of Line…

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Q: | 23. Find the outward flux of the field F = ( 3xy i + (e* + tan¯ly)j х 1 + y?, across the cardioid…

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Q: Problem 4. Calculate the lux F. dS of the vector field F = (0,0, 1) across the hemisphere S: a? + y?…

A: According to the given information, it is required to calculate the flux of the vector field F…

Q: Question 19 Find the flux of the vector field F = k through the upper half of the sphere x2 + y² +…

A: As per the guidelines I solved your first question complete. For more solutions please repost the…

Q: Problem 2. Let F be the vector field (re² + cos(x), –ye², z sin(x)), and S the paraboloid z =1-1² –…

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Q: Problem 2 CONSERVATIVE VECTOR FIELD -I -Y The vector field F(x, y) = \(x² + y²) (2² + y²)/ is…

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Q: In Problem 3, find the flux of the given vector field F through S according to the described…

A: Given data:  Vector field F→=yi→+2xj→+3zk→ S is the portion of the cylinder Radius of cylinder…

Q: By experiment, you find that a force field F performs only half as much work in moving an object…

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Q: (1) Let F(x, y) = (2y³/2, 3x√√y). (a) Show that F is a conservative vector field. (b) Find a…

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Q: 11. Find the flux of the field F =ri – yj across the curve C: r(t) = (cos t)i+ (2 sin t)j, 0 <t< 2n

A: Given vector field is F=xi-yj across the curve C:rt=costi+2sintj , 0≤t≤2π Flux of the vector field F…

Q: Question 2 Find the flux of the vector field F across the surface S in the indicated direction. F =…

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Q: (a) Suppose that F is an inverse square force field, that is ,  F (r) =cr/|r|3 for some constant c,…

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Q: Question 3 (a) Evaluate f. 5(y – 5)dx + (8x + e sin 2)dy where C is the triangle with vertices…

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Q: Consider I = ∫CF⋅dr, where (img17) is a conservative vector field and curve C is parameterized by:…

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Q: QUESTION 7 What is the value of a so that the vector field F(x.y)=(2xy+y3) i+(x²-axy-4) j is…

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Q: Question 3 Consider the vector field v(x) = i+ i+ 6k. y j + 6k. Vx²+y Vx²+y² a) Calculate /v• dr,…

A: Given vectors is vx=xx2+y2i+yx2+y2j+6k To evaluate ∫Cv·dr where C is the line joining (8,0,8) to…

Q: Question 3 (2y +z z2 Give line integral of vector field v(x,y,z) = along curve y: ř(t) = | -t),t E…

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Q: 3. Given a potential field V= 10r sin² 0 cos ɖ (a) Find flux density D at (3, T/4, t/6) (b) Dose the…

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Q: For Problem 2, calculate the flux of the vector field F through the given surface S. 2. F = -4i+…

A: Given F→=-4i^+xj^+2zk^ and S:x+2y+z-2=0

Q: 1. Suppose that C is the top-half of the circle (x-a)² + y² = a², (a > 0) oriented in the…

A: Please see the below picture for detailed solution.

Q: YouTrylt 5 Calculate the work done by the force field F= (sinx-6x°y,3xy –: particle from the origin…

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Q: Question A1 Consider a vector field F= 2x° yị +x'j., and a curve C defined by the equation y = 2x².…

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Q: Question 6 Consider the scalar field f(z, y) = (x + ;)(2² + 3z +y²) on the set D = {(z, y) | 2² +y²…

A: Given function is  fx,y=x+32x2+3x+y2=x3+32x2+3x2+92x+xy2+32y2                =x3+92x2+92x+xy2+32y2…

Q: Problem 5. Use the Divergence Theorem, F. dS = div F dV, E to calculate the flux F. dS of the vector…

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Q: Problem 2. Let F be the vector field (xe² + cos(x), -ye², z sin(x)), and S the paraboloid z = 1- x2…

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Q: Problem 4. Consider the vector field in R? F(r, y) = (yey + ry²e=, rey +x?ye#") Netermine if the…

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Q: Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² -k².

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 19. (a) Evaluate the line integral F. dr, for F(x, y) = ex−¹ i + xy j and C is given by r(t) = t² i…

A: (a)F(x, y) = ex-1 i + xy j   And C: r(t) = t2i +t3j , 0≤t≤1.⇒drdt = 2t i + 3t2j and F(r(t)) = et2-1…

Q: Question 2. Solve the equation ug + Uy + u = e®+2y with the initial condition u(x, 0) = 0. (Both…

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Q: Question 9 Please state a, b, c, d, e, f Consider the velocity field v = –yi+x²j+z²k. Evaluate the…

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: Question Number 5: i) Find the divergence and the curl of the vector field F(x, y,z) = (xi + yj +…

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Q: Question 2 The out-flux of the vector field F(r, y, z) = (sin(2.r) + ye, (y + 1)², -2z(y+ cos(2a)…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Calculate the flux of the field F across the closed plane curve C. F=xi+yj, the curve C is the…

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Q: Question 6 (C15.3) For the vector field function, F (x, y) = 9x² y²i + (6x³y – 1) j and an object…

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Q: (a) Suppose that you are asked to determine the path that requires the least work for a force field…

A: For Conservative Force Field  amount of work it takes to move a particle from one point to another…