4. Let X = x Ә ду the Lie bracket Ә у and Y дх [X, Y]. Ә = z= +y дх Ә be differentiable vector fields in R³. Calculate ду

Q: OV.F 7 (V.F) VX (V x F) O (Vf) x F (V.F). F

A: It is given that the function  is a scalar valued function and  be the vector field function.Check…

Q: Find r'(t), r(t), and r'(t) for the given value of to. Then sketch the space curve represented by…

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Q: xy² (0) (Use syntax like [3,-4,5] for vectors.) Let F (x, y, z) = xz5 What is the value of curl F at…

A: The vector F(x, y, z) is given. We have to find the value of curl F at (3, 2,1) .

Q: Let f(x, y) = x^2/(x + y). Find a unit vector u such that Duf(1, 2) = 0

A: f(x, y) = x^2/(x + y)

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

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

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector - [';" - a 1 - ] a P = b

A: From the given information, P=1-aab1-b Let, stable vector as, w=xy

Q: Compute the flux of the vector field (4, - y²), out of the rectangle with vertices (0,0), (2,0),…

A:

Q: Find the flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

A: A constant vector field  and a square plate of area 25 in the xy plane oriented in the positive z…

Q: Show that the gradient vector is perpendicular to the tangent at a point of an isovalue curve

A: According to question                                     Let,  w=f(x, y, z)  be a function in…

Q: Compute the flux of the vector field (x², - xy³), out of the rectangle with vertices (0,0), (5,0),…

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Q: FTTT 10 5 10- -5- -10- X TTTTI 1C d.

A: We draw the sketch of vector field with the help of direction and length of vectors .

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: 2 Locate the numbers z₁+z₂ and z, - z₂ vectorially when z₁ = 2i, z₂ ==-i. 3

A: Use addition the evaluate these numbers then plot it

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: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

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Q: A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of…

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Q: Find the curl of the vector field F =< yx5, xz², zyб curl F = i + 1:0 12

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