Throughout this question we will be talking about the vector field F = (cos(y²), xy + z, x²y + xz). (a) Find the divergence of the vector field F: div F = (b) Is there a vector field G such that F (c) Find the value of the flux integral J₁₁ curl G? Explain how you know. FdS where S is the surface of the tetrahedron bounded oriented with outward facing normal by the planes z = = 0, x = 0, y = 0 and z = 1 vectors (see figure). 2 Y 2

Q: F(x, y, z) = (x²)Î + (2y³2)ĵ + (32)Â is a vector field. (a) div(F) (b) curl(F) (c) C is the…

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Q: ) Let C be the path r(t) = (sin(t), te', cos(t)), 0 <t < . Calculate F. dr.

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Q: In Cartesian coordinates, a vector field takes the form F = 2rz i+2yz j+ (z + y?)k (a) State whether…

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Q: 4. Consider the vector field F(r, y, z) = (x, y, z). (a) Sketch a picture of F. (b) Calculate div F.…

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Q: If a vector field F (x, y, z) = (y² + z², xe cos z, - xe³ cos z), which of the following values is…

A: Given vector field is Fx, y, z=&lt;y2+z2, xey cosz, -xey cosz&gt;.   To Find: div F.

Q: . Let F be the vector field (ze"z + yz², xz², xe*z + 2xyz) (a) Find the divergence of F. (b) Find…

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Q: Let I be the curve parametrised by 2t 2(4) = ( sin(zt), 41' Vt +1 for 0<t<1 t2 +1' and let F be the…

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Q: Consider the line integral (Image 1) , where C is defined by the vector function: r (t) = - t2i +…

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Q: Given the vector field F = (r + y)7+ (r – y)7, evaluate it's line integral over the plane curve a? +…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: is the part of the cone between

Q: (d) Is F a conservative vector field? Justify your answer.

A: given: F→=(zexz+yz2, xz2, xexz+2xyz)