Let S be the square in the zy-plane shown in the figure below, oriented with the normal pointing in the positive z-direction. Estimate J.F. where F is a vector field whose values at the labeled points are @THE 2 5° JF-dS #00 Go F(A) (-2,-7,5), F(C)(-9,7,5), FdS F(B) - = (9,-1,-8) F(D) = (1, -3,3)

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: x-y, z + y + 3,z²) and the net is decribed by the equation y = 1- x² - z on

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Q: When is the vector field continuous?

A: given,       Continuous vector field .

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Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

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A: Given:The vector field  is given by .To Find:We have to sketch the given vector field.

Q: The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end…

A: Given, vector field F→x,y=2xy,x2 and three curves that start at 1,2 and end at 3,2.

Q: Given the vector field F = (In(x + 2z), xy, xyz). Calculate curl F(-1,1,1).

A: Solution:-

Q: Q3 Check the symmetry and graph the curve in polar form if 0 = 0 and equal 1/6 to 1/2 at increments…

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Q: Consider the vector field v(x)=(y/(x^2+y^2))i − (x/(x^2+y^2)) j + 4k. Calculate ∫Cv dr, where C is…

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A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: 13. For the vector fields: A = x + 2y ŷ + 3z 2; B = 3y - 2x ŷ. Check both product rule given in…

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Q: Find the gradient vector field of f(r,y, z) = x*y* +y³z³ + æz°.

A: The gradient vector field of f(x,y,z) is given by ∇f=∂∂xf(x,y,z) i^+∂∂yf(x,y,z) j^+∂∂zf(x,y,z) k^…

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Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

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Q: Find the curl of the vector field F(x,y,z)=x^2yi-2y^3zj-3zk.   A. curl F = 2y3i + x2k          B.…

A: Option (c) correct  For detail...go through the solution

Q: The gradient vector field of f(x,y)=y(2x2 -y3 ) is given by: O1. (2xy)i +(x2 -3y² »i O II. (4xy)i…

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Q: Find the curl of the vector field F = (3y cos(x), 5x sin(y))

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Q: Show that the vector field F(x, y, z) = (-ycos(8x), 8x sin(-y), 0) is not a gradient vector field by…

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Q: Show that Vx (V.f) = 0 for any vector field f.

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Q: (a) Consider the vector field G = (xyz, yz, xz). Find div(G). (b) (1,2,3). Using the G from part…

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Q: 1. Let F =i+y^2j +z^4k. Find the general flow lines for this vector field. Present the flow line…

A: Consider the provided question,

Q: Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve that consists of two line…

A: Given that  Fx,y = xy2+2x+1 , x2y - 3y is a vector field. Let C be the curve that consists of two…

Q: Find the curl of the vector field F (6x sin(y), 2y cos(x)). curl F =

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Q: Please answer and write correctly and neatly. Given the vector field Ā= 2x2y ax – 2(z-x) ay + 3xyz…

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A: When the field vectors are going the same direction as the vectors normal to the surface, the flux…