A conservative vector field is given by F=(-z-1)i + (-2y+2)j + (-z-1) k. Select two options that give a potential function for F Select one or more: U(z, y, z) = 2xz+x+3² − 2y+z DU(z,y,z)=x+2y+z U(z. y, z) = zz + x + y² − 2y + z U(x, y, z) = (x + 1) (z+1) – (z − 1) U(a, y, z)=(-2-1)-²-2y-z(-z-1) WINE

Q: If r(t) = u(t) x v(t), where u and v are the vector functions given below, find r'(2). u(2) = (6, 3,…

A: To find r'(2).

Q: C

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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…

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Q: Find the gradient vector field of f(x, y) = ln(5x + y)

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Q: Let r(t) = 5e7t + e2t and y(t) = 3e2t + 1le (i) Rewrite the given functions in the vector form Y(t)…

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Q: Show that (u - v) × (u + v) = 2(u × v)

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Q: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

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Q: 2. For the vector field F(x, y, z) = (x²y, xyz, −x²y²) F(x, y, z)=(x2y,xyz,-x2 y 2 ), find: (a) div…

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Q: Compute fa(P) where is a unit vector in the direction of . a) f(x, y) = x² + 2xy + 3y², P = (2,1), v…

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Q: For the vector-valued function r(t) = t³i + (2t² + 1)j + (3t − 6)k find the following and express…

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: -(4,2) use it to evaluate F. dr (1,0)

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = √3x² + 4y² + 2². F(x, y, z) =

A: Solution:-

Q: Consider the vectorial V=2+ŷ+ 2 z . . function=z²+x²y + y²2 and the gradient operator Please…

A: Given that the vectorial function ψ→=z2 x^+x2 y^+y2 z^ The gradient operator ∇→=x^.∂∂x+y^.∂∂y+z^.∂∂z…

Q: Evaluate the 1-form φ = x2yz dx − z dy on the vector field V (x, y, z) = xU1(x, y, z) − yzU2(x, y,…

A: We need to evaluate the 1-form of  ϕ=x2yz dx - z dy.....(1) in the vector field  V(x,y,z) = x…

Q: Determine if the vector fields below are conservative. Find potential functions where possible. (a.)…

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Q: (c) Calculate the divergence (V.Ä = div Ã) and curl (V × Ā = rot Á). of the following vector fields.…

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Q: Find a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y)

A: we have to find potential function.

Q: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

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Q: If the following vector function are equal to: A(t) = 5*t i + 2*t^2 j B(t) = 3*t^2 + 2 j Then…

A: The given problem is to find the derivative of the dot product of the two vector functions. Given…

Q: Calculate vector field F = (2-z²+2-x²)i + (2 · y³ + 4·x)j + (2x²z³+2)k a flux from a box with the…

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Q: reply as soon as posible.

A: To find out the conservative.

Q: Determine whether or not F(x,y) = (xy + y²,x² + 2xy) is a conservative vector field.

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

Q: Let F₁ (x, y, z) = (y, x-z²+2, -2yz) and F₂(x, y, z) = (x − z², -y +2, 2yz). (a) Find the curl of…

A: Given vectors  and  we need to find the curl of each vectors and then determine which vector is…

Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

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Q: Given two vector fields E = 5xya, + 6(x + 3)a, + 8z'a, D = yza, + xza, + xya, (a) Evaluate C= D+E at…

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Q: re f an -2, 3)

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Q: 6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z,…

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Q: F(x,y) = (4xy. – 3y²) (A Vxi = -4x B) V XF - - 2y C vxF V xF - - 2y + 8x D VxF - 4x - 6y

A: solution