For the vector field F(x,y,z)=ya'1+x1+2xyz k a) show that F is conservative vector field; b) find a potential function for F <) evaluate [F-dr where is the line segment from A(0,0,1) to 8(1,3,2)

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Q: 2) For the vector field F(x, y, z)=(xz²-x²y)i + (xy²-y³2²)] +xy²z³k, find the following: a) Find the…

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Q: Find the curl of the vector field F. F(x, y, x) = 2yz'i + 3xj +&xk O 15r4 O 15:3 O (8yz – 8]j +…

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Q: Find the curl of the vector field F = <yx³, xz³, zy² curl F = i + k + V

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Q: d) Use the curl test to determine if the following vector fields are conservative on R². If the test…

A: As per our guideline we can solve only first three subparts question. Let a vector field    F=…

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Q: Suppose F = (P(x, y, z), Q(x, y, z,), R(x, y, z)), is conservative vector field. Here P, Q, R are…

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Q: point -2 has parameterization F(t) = (4(1-t), 3t) for 0 s 2

A: This is a problem of vector calculus.

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Q: 11. LetF(x, y) = (ye™ – 6x))i + (xe™v + 4)7 (a) Show that F~ is a conservative vector field. (b)…

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A: Answer:   The correct option is B.

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Q: let 2 Vector tield A=x B=y2 Find explicit expresom of Lie derivative L, CB)

A: Please find the answer in next step.