Compute the flux of the vector field F(x, y, z) = 3i + 2j + 2k through the rectangular region with corners at (1, 0, 0), (1, 1, 0), (1, 1, 2), and (1, 0, 2) oriented in the positive x- direction, as shown in the figure. Flux = 0

Q: Find the flux of the vector field F = (y, z, x) across the - part of the plane z = 4+3x+2y above the…

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Q: F(x, y, z) = -k At (-2,-2, -2) the vector is At (-2,-2, 2) the vector is At (-2, 2, -2) the vector…

A: Given vector field F(x,y,z)=-k Here k is constant

Q: Compute the flux of the vector field F(x, y, z)-6i+6j+ 4k through the rectangular region with comers…

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Q: Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the…

A: v→=y2i→+1.3x2j→ Initial point 1,2 ∆t=0.1

Q: 1) Find the work done by the vector field F(x, y, z) = (x², 4xy³, xy²) on a particle that %3D…

A: Given force is F→x,y,z=x2,4xy3,xy2 Let r→=rt→ be the boundary of the rectangle with vertices  0,0,0,…

Q: Find the curl of the vector field F = curl F = 12 + j+ k

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Q: Sketch several representative vectors in the vector field given by F(x,y)-3yi-xj. b. a. 3 34

A: F(x,y)=3y i - x j F(0,1)=3(1) i - (0) j=3iF(1,0)=3(0) i - (1) j=-jF(-1,0)=3(0) i - (-1)…

Q: Compute the flux of the vector field (ï³, — xy³), out of the rectangle with vertices (0,0), (4,0),…

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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: Find the flux of the vector field F = across the part of the plane z = 3 + 2x + 4y above the…

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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: 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^…

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: Find the flux of the vector field V(x, y, z) = 2xy²i+ 5x²yj + 3z³k out of the unit sphere. Flux =

A: Denote the unit sphere by S If the sphere is closed,  then the flux of v(x, y, z) out of S is given…

Q: Consider the vector field F = (2, -3). Let C be the straight line segment oriented from point (3,0)…

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

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