Q3:A force described by -xx zz yŷ 2 x+y2+: + 2 x²+y 2+y 2 2 2+z 1- Express F in circular cylindrical coordinates. 2- Calculate the curl of F F is conservative or not. 3- Calculate the divergence of F .

Q: Compute the curl and divergence of the vector field F(x, y, z) = (T 2², 2yz) . Is F conservative? If…

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Q: Confirm that the force field F(, y) = 2xy°i+ 3x²y² j is conservative in some open connected region…

A: Solution:- The given function is  F(x,y)=2xy3i+3x2y2jpoint P(-9,8) and Q(6,7)we have to find the…

Q: Find the workdone in moving a particle in a force field given by f=3xyi-5zj+10xk along the curve…

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Q: 4. Find the divergence and curl of the following vector function: F(x,y, z) = ( arctan(ry),…

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Q: The given vector function is F(x, y, z) = (2x – y + In(z² + 1))î + (x – 6e²y + 4 cos 4y)ĵ + | 2xz -…

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Q: Confirm that the force field F = xy²i + x²yj is conservative in some open connected region…

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Q: Let divF(x,y, z) = 4x³ + 4y³ + 42³ , where F represents the flow of a vector field. Estimate the…

A: Concept Used:- Divergence Theorem Flux=∫∫∫∇.F dVwhere ∇.F is the divergence of FVolume of the…

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: From the given vector field F⃗ (x, y, z) = , compute the curl of F⃗ and find the values of a and b…

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Q: Let S be the sphere x^(2)+y^(2)+z^(2)=4 with outward normal vector. Use the divergence theorem to…

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Q: 3. Use Green's theorem to find the work done by the force field F(x,y) = xyi + (;x² + yy)j on a…

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Q: 1. Use the divergence theorem to evaluate the surface integral F · dS, S where the vector field is F…

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Q: Let = (xz, 2 4xyz, rz) be the velocity field of a fluid. Compute the flux of i across the surface…

A: Flux of velocity about a surface is the measure of amount of velocity of fluid hitting the surface.…

Q: 4. The vector field F(x, y) = (x² – y²)i+ 10-Rj-2zrk represents the velocity of a gas flowing in…

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Q: (x²z, 2 – 4xyz, xz²) be the velocity field of a fluid. Compute the flux of v across the surface 4x2…

A: Given velocity field.

Q: Q3:A force described by -xx yŷ zz F- x2+y 2+z 2 x 2+y 2 +y²+z 1- Express Fin circular cylindrical…

A: Given force is, F⇀=-xx^x2+y2+z2+yy^x2+y2+z2+zz^x2+y2+z2. 1.) In cylindrical coordinates,…

Q: Let F be the vector field F(r, y, ) = =i- sin yj+ (2r: +6:)k. Compute divergence and gradient of the…

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Q: Q3. Consider the vector of electric field E(x,y,z) = (sinh x)i – (cosh y)j – xyz k a. Compute the…

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Q: Let v (2, y sin z, cos z) be the velocity field of a fluid. Compute the flux of v across the surface…

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Q: Find the divergence of the vector field F→(x,y,z)=7sinxi→−cos(3y)j→+z^9k→.   Enter the exact…

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Q: Consider the vector of electric field E(x, y, z) = (sinh x)i – (cosh y)j – xyz k a. Compute the…

A: The given vector field is, E(x,y,z) = (sinh x) i - (cosh y) j - (xyz) k   the divergence and curl…

Q: Find the work done by the force field F(x, y, z) = (x – y², y – z?, z – x2) on a particle that moves…

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Q: Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of…

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Q: Find the flux of F over the surface S of equation z2 = x2 + y2 , 0 ≤ z ≤ 3 and parameterized by x =…

A: Let E be a three-dimensional solid bounded by a piecewise smooth closed surface S that has…

Q: Find the work done in moving a particle in the force field F : 3x²i + (2xz - y)j + zk along the…

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Q: Compute the flux of the vector field F == through the surface S where S is the surface bounded by r…

A: Given thatF→=fr,fθ,fz=r2+sin2θ,rsincosθ,3z∂∂rrfr=∂∂rr22+sin2θ=2r2+sin2θ& ∂∂θfθ=∂∂θr…

Q: Confirm that the force field F = xy²i + x²yj is conservative in some open connected region…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F =x3y 2i+yj…

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Q: Q4(b) Given the force field F(x, y, z) = (z^3 – 2xy)i – x^2j + 3xz^2 k (i) Show that F is a…

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Q: Q.3) Use the divergence theorem to find the outward flux of the vector field F(r, y, r) = ri %3!…

A: Here, Fx,y,x=xi

Q: Let v = (5, y sin z, cos z) be the velocity field of a fluid. Compute the flux of v across the…

A: Given, v→=5,y sinz, cosz Flux=∫∫Sv⇀.ds we have divergence theorem, ∫∫Sv⇀.ds=∫∫∫Sdiv v⇀.dv div…

Q: Let divF(x, y, z) = 4x³ + 4y3 +4z³, where F represents the flow of a vector field. Estimate the flux…

A: Given divF→x,y,z=4x3+4y3+4z3radius r=0.1 Centered at point 1,1,1

Q: Compute the work done by the force field F = 6.2y" i + 6.2a" j on a particle moving along the…

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Q: 5/ MATH

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Q: ul for the through the box [o,8] x[ 0,41 x[0,2]. vector field f=<z,x, y2, calculate the rotalflux S.…

A: We need to calculate divergence . The formula for divergence for F=&lt;P,Q,R&gt; is ,…

Q: Q3 (a) Calculate the divergence of curl of vector F = e2z+y î + sin yz² j+cos yzx k, V· (V × F). (5…

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Q: Q3. Consider the vector of electric field E(x, y, z) = (sinh x)i – (cosh y)j – xyz k a. Compute the…

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Q: If F = xy i+ (x² + 4yz)j+ 2y²z k. Evaluate the line integral between A (0, 2, 0) and B (3, 6, 1).…

A: Given, F= xy i +(x²+4yz)j +2y²zk r0= (0,2,0) r1= (3,6,1)

Q: Find the divergence at (15, 0, 0) for the vector field F(x, y, z)= e*sinyi-e cosyj+z²k O 16 O 451 30…

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Q: Calculate the work done by the force field F(x,y, z) = [x² + 10z² i+(y² + 14x² ]j+ z² + 12y² ]k +…

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Q: Confirm that the force field F(c, y) = 2xy³i + 3x?y?j is conservative in some open connected region…

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Q: Let divF(x, y, z) 4x3 + 4y3 + 4z³ , where F represents the flow of a vector field. Estimate the flux…

A: Given that a small sphere of radius 0.1, centered at the point  (1, 1, 1).And                  div F…

Q: Compute the flux of the vector field F(x, y, z) = 41 + 45 + Sk through the rectangular region with…

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Q: 21. Compute the flow of the vector field F = r through the surface of the ellipsoid y² + 2 = 1 in…

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Q: Exercise (3): Find the work done under the influence of the force F = 3xyi – 5zj + 10xk along the…

A: The work done by a force on displacing a object by a certain distance is given by dot product of…

Q: Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of…

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Q: Find the flux of the vector field F = (y,- z, z) across the part of the plane z = 4 + 3z + 2y above…

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Q: Calculate of A= Xzi- 2x*yzj+2yz'K at ( 1,-1,2). the Curl and Divergence

A: Given A = xz3i-2x2yzj+2yz4k Compare it with A = Axi+Ayj+Azk Hence Ax = xz3Ay = -2x2yzAz = 2yz4 Then…

Q: Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of…

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