(10) Given that the vector field F= 2z i- 3 x j + 4 y k Evaluate f F. dr where S is the portion of the paraboloid z = 16 - x² - y? for z 2 0 in the first octant

Q: What is the (numerical) value of the 3-form field (x² + y + z?) dx A dy A dz on the ordered triple…

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Q: 5. Consider the vector field F(x,y,z) = yzi + xzj+(xy+2z) k and the curve C given by r(t) = (t+ sin…

A: Given vector field: Fx,y,z=yzi+xzj+xy+2zk Curve C is given by: rt=t+sin12πt,t+cos12πt,2t,   0≤t≤1…

Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 6. Let F = (x³ sin y, a* cos y). COS (a) Is F a conservative vector field? (b) If your answer to…

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Q: 13 Given the conservative vector field, F = (x +3y?)i +(6.xy +5)j , evaluate the 120) integral F.ds…

A: Here we use the way of line integral. By finding the parametric path between two points.

Q: 9. Compute the flux of the vector field F(x, y) = (-x sin(1+xy) – 4 cos(TY), y sin(1+ xy) + 6x)…

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Q: Find the potential function for the following vector field F(x, y, z) = (2xy – 29) î + (x² + z²)j+…

A: To find the potential function, f, integrate each partial derivative. Integrate ∫fxdx=∫(2xy-29)dx,…

Q: Q3) Compute the work done by the force field F(x,y,z) = (3x, xz, y) on the curve C, where C is the…

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Q: Q3 Given the conservative vector field, F =(x +y²)i +(2xy +5)j , evaluate the integral F•ds where C…

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Q: Given a vector field F = 5(x² + y²)i+ 2xyj - 3zk, evaluate SSS, V· FdV for which the solid D is…

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Q: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

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Q: Q3 Given the conservative vector field, F = (x +y²)i +(2xy +5)j , evaluate the integral F•ds where C…

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Q: 5. Find the potential function for given vector field: F = (e* In(y))i + + sin(2))j + ycos(z)k

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Q: Q4 A) Calculate the divergence of the vector field F=y³i + xyj B) Find the Curl of F(xy.z)=3x²i +…

A: To find out the divergence of vector field.

Q: 8. The component of the field F= (1,2,3) normal to the plane z = -3x + 3y -1 is (a) 0. (b) –2//19.…

A: If we are given a plane equation in the form Ax+By+Cz=D, then the normal vector to the plane will…

Q: 1. Consider the vector field F(x, y, z) = (2e2" cos(3y), –3e²" sin(3y) + Y a. Find divF(x, y, z) and…

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Q: a) Is the vector field F = (a2 - yr, y?- xy) path independent (conservative)? %3D O True O False b)…

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Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzĵ + xyk in moving from (1,1,1) to…

A: The equation of a line joining by the points and is given as the following.

Q: Find the work done by the vector field F = (– 4z, – 3y, – 2x) in moving an object along C in the…

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Q: 8. Given the vector field G(x, y, z) = e>+2z (1 + x j + 2xk) : a) Show G(x, y, z) is conservative…

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Q: (b) Given a vector field F = 5(x² + y²)i+ 2xyj – 3zk, evaluate JI, V· FdV for which the solid D is…

A: Here we use polar form of circle .

Q: 2.) Calculate the curve integral over the vector field V(17, y) = ( * -2²y xy? for the positive…

A: Disclaimer: Since you have asked for a handwritten solution and currently we are not providing any…

Q: 3. Consider the vector field F = 2xy i + (x² + 2y) j. Verify the Green's Theorem in the closed…

A: Definition of green's theorem :

Q: 2) Given the vector field F = (- Vx²+y² 2z2) write the integral to calculate the outward x²+y² flux…

A: We have to find the outward flux across the cylinder x2+y2=100.

Q: The circuitation of the vector field F(x, y)- (3 + xy´, 4x + xy) along the boundary of the plane…

A: The solution are next step

Q: Is the vector field F(x, y) = (sin(x)ely=3 + 2r cos(r>)y°, -2e)y-3 + 6 sin(x³)»*) conservative?…

A: Consider the given vector field.

Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = Jx2 + y2 + 3 that…

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Q: (c) Determine the flux of the vector field F = x³i – 2yĵ + 7z²k across a cone z = x2 + y2 + 3 that…

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Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = J 8 by using…

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Q: 2. Given F(x, y) = (4x³y² - 2xy³)i + (2x¹y − 3x²y² + 4y³)j is a - conservative vector field. a. Find…

A: To find the potential function for the given conservative vector field :-

Q: Зу 1. Given the vector field F(x, y, z) = î+ Vrz j+x cos y - k, find curl F and div F.

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Q: 3. Consider the vector field F(x, y) = (2xy, x² – sin y). Evaluate %3D F. ds where C is the curve…

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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: Ex: Find the work done by the vector field F = (y-x²)i + (z - y²)j + (x-z²2)k Over the curve r(t) =…

A: Given: F=y-x2i+z-y2j+x-z2krt=ti+t2j+t3k

Q: Consider the vector field F (xr, y) = (2y - 12r*y", 4ry – 9r*y?) is conservative. (a) Show that F…

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Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzj + xyk in moving from || (1,1,1) to…

A: The given question is related with work done. We have to find the work done ∫CF→ . dr  in the force…

Q: If F = (4xy – z³) î + 2x² ĵ – 3xz² k is a conservative force field, then scalar potential of F is…

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Q: Find the potential function for the following vector field F(x, y, z) = (2x cos y – 2z3) î + (29+…

A: F = <2xcosy-2z3, 29+2ye2-x2siny, y2e2-6xz> To check F¯ is conservative  not we have t check…

Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: 5) Integrate the vector field h a,y)= y2i+ (2xy-e*)J C parumetrizal by t€ £0, 5 3. over the circular…

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Q: The vector field F(r, y) = (2xy +y) dx + (æ + 2xy) dy is conservative. %3D The function f(x, y) = x²…

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Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

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Q: 3. For the vector Field E = -(x² + 2y²)âx + (xy)ŷ calculate E dl around the triangular contour (V×…

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Q: Given the conservative vector field, F=(x +y³)i +(2xy +5)j , evaluate th Q3 integral | F•ds where C…

A: Given a conservative vector field, F=x+y2i+2xy+5j. Here, M=x+y2 and N=2xy+5. Since, F is…

Q: Consider the one-form w = x' cos(y) dx + xe13% dy+4z² dz on R3. The associated vector field is: F(x,…

A: For the solution follow the next step.

Q: Consider the vector Field 7 and the curve C below. F(x,y) = (3 +4 ху?) 1 + 4x²yј, C is the arc of…

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Q: Given vector field F(x, y) = (4x³y? – 2xy³,2x*y – 3x?y² +6y³) and curve C defined by C: 7(t) = (t+…

A: Here we will find out the required value.

Q: 4. Given the vector field Č = p² sin o a, + (z² cos – 1)as + (p² – z)a, Determine the x-component of…

A: Given the vector field