Consider the scalar function (x, y, z) and the vector field F(x, y, z) defined as . (x, y, z) = 3zx² + 2xe³ - In(xz) F(x, y, z) = −3zx³7+5y²+4yzk (a) Evaluate V · Vò̟. (b) Evaluate V x (▼ × F). (c) Calculate the directional derivative at the point P function (x, y, z) in the direction ▼ × (▼ × F). = (1, 0, 1) of the scalar (d) Determine the equation of the tangent plane on the level surface at the point Po = (1, 0, 1). = 5

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Q: Q4 A) Calculate the divergence of the vector field F=y³i + xyj B) Find the Curl of F(xy.z)=3x²i +…

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A: Given :- F →t =  cos πt , e2t-1 , t2 - 1  , G →1 =  1 , 1 , -1G' →1 =  2, 3, 2G'' →1 =  0 , 1 , 0…

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A: Given vector field is  Fx,y=xy+y2,x2+2xy Fx,y=F1,F2 A vector field is said to be conservative if…

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A: Given that    Fx,y,z=8x cosy sin2z+2e2xz i^-4x2 siny sin2z j^+gx,zcosy+2e2xz k^ Now we have to find…

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