Find the Curl of the vector field. F(x,y, z) = 7e" sin(yi+ 8e* cos(y j+ 14z k a. &e" cos(y) +7e" cos(y)]k Ob (8e" cos(y)) k COS Oc (et" cos(y)– 7e" cos(»)) * -(4)sa + 7e* sin y)]k C. COS k Od. "(se" sin(y) O e No correct answer

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Q: When is the vector field continuous?

A: given,       Continuous vector field .

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Q: 2. Show that V(V × F) = 0, here vector field is twice differentiable. %3D

A: This question is from vectors.

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A: Given,F(x,y,z) = -19y3i + 19x3j + 7k⇒curl F = ijk∂∂x∂∂y∂∂z-19y319x37          = 0i + 0j +…

Q: 1. Verify the Divergence Theorem in the calculation of the flux of the vector field: through the…

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Q: Compute the flux of the vector field (x2, - xy*), out of the rectangle with vertices (0,0), (4,0),…

A: Given,

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A: According to question,Given vector field,F→x, y, z = 2xx2 + cos z-y322x, -32xy+z, -sin zx2 + cos z+y

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Q: Provide two examples of physical phenomena in which the divergence of a vector field is nonzero.

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Q: Find curl F for the vector field at the point (3, -9, 1). F(x,y,z) = x2zi - 2xzj + yzk curl F %3D

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Q: 4. Verify that the two integrals in the circulation form of Green's Theorem are equal along a circle…

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