F(x, y, z)= 400 x² +2² 5(x, 0, z). 1. Compute the curl and the divergence of F. Explain what each of the results mean about F.

Q: Explain Divergence of curl of B.

A: Let f = f1i+f2j+f3k Then curl(f) is given by ∇×f = ijk∂∂x∂∂y∂∂zf1f2f3=…

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Q: O {1, z+ 3, 2a, sinz In 2,1

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Q: 9. Find the curl and divergence of F. (xy)i + (yz)j + (xz)k а. b. (ze*)i + (y²e*)j+ (xy³e*z)k

A: Curl and divergence of F

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Q: 18)Find curl F and div F if F(x,y,z) = exsiny i + esinz j + e²sinx k

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Q: (15) Given two functions u(x + y) and v(x + y), what is Vu × Vv? Don't show it using an example. If…

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Q: se the given transformation to evaluate the integral. J 6z + 3ydA, where Ris the parallelogram with…

A: we have given: x=13u+v and y=132u-v  u=x+y, v=2x-y Now, Consider the integrals, ∬R6x+3ydA where, R…

Q: F(x, y, x) = i + 3xj + 2yk And G(x, y, x) = xi - yj + zk. Find the Curl(FxG).

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Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: If F(x, y, z)= xz i  + xyz j - y 2 k find curl F

A: given: F(x,y,z)=xzi+xyzj-y2k we have to find the curl F. as we know that if we have F→=Fxi+Fyj+Fzk…

Q: Is there a vector field Ğ on R³ such that curl Ġ = (xyz,–y*z³,y*z*)?

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Q: Prove that the divergence of a curl is always zero. Check it for function va = x2x-hat + 3xz2y-hat −…

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Q: If F = Pi+Qj+ Rk, prove that div (curl F) = 0

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Q: If F = xyz i+ zxj +xy'z k then find curl F at (1, 2, – 1).

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Q: Find curl(F x G) = V x (F x G). F(x, y, z) = i + 9xj + 7yk G(x, y, z) = xi - yj + zk

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Q: Find the divergence of the field. F = 3ye5xyzi + 3ze5xyzj +3ye5xyzk

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Q: - Suppose S₁ F. dr #S, F. dr where C₁ and C₂ are two distinct piecewise smooth paths from (0,0,0) to…

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Q: Prove that the divergence of a curl is zero.

A: Our aim is to prove that the divergence of a curl is zero.