b) A vector field is given by F = (2xy + z³)i + x²j+ 3xz²k i) Show that the vector field F has the property that curl(F) = 0. What is the physical significance of this? ii) Determine a scalar potential field such that F = Vo.

Q: 2. Sketch at least ten arrows in the vector field: F(x,y)=(-2y)i + (x+1)j

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Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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Q: Find the directional derivative of the scalar field = x³y + 4xz at the point (1,-1, 2) along the…

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A: Solution:-

Q: Find the flux of the vector field V(x, y, z) = 9xy²i + 9x²yj + z³k out of the unit sphere.

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Q: Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.

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Q: (c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given…

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Q: (9) Let F Be a vector field over ø be a scalar field. Prove the following similarity: V. (OF) = (Vo)…

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Q: Find the curl of the vector field F = curl F = i + 3 12 רז k

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Q: Q1: a) Sketch the vector field and find the fixed points of the following function i = x - V1 -…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…