Verify F(x, y, z) = (2y + z)ê + (x – z)j + (y – z )k taken over a triangle cut from the Stokes' theorem for the vector field - Z plane x+ y + z = 1 by the coordinate planes.

Q: Express the vector field W = (x2 - y)a, + xza, in the (a) Cylinderical coordinate at P(p = 6, q =…

A: Cylindrical coordinates are ρ,ϕ,z now let us look at the general form of vector fieldW in…

Q: Consider the force field F(x, y) = (x, y). a) Sketch the vectors F(1,1), F(-2,1) and F(2,0) directly…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ye F(x, y, z) =

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Q: 2. Let C be the curve of intersection between the cylinder r2+y = 1 and r-2y+z = 0, oriented…

A: The complete solutions are given below

Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

A: As per Bartleby guidelines I have authority to answer only one question. If you want other…

Q: Suppose the vector field v(x, y, z) = (4xy2, -4xz², 5x) represents the velocity field of a fluid.…

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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^…

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: 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: Find the gradient vector field (F(x, y, z)) of f(x, y, z) - F(x, y, z) = z Cos 5z

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Q: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

A: Given: F→=xi→+yj→ z=36-x2+y2 ds=1+∂z∂x2+∂z∂y2dxdy       =1+4x2+4y2dxdy   and…

Q: The work done by the vector field F(x, y) = (-y², ²) along the arc of the parabola y = 2x² - 4x + 2…

A: According to question,Given Vector field,Fx, = -y2,x2Equation of pparabola,y = 2x2-4x+2

Q: Let us verify Stokes' theorem using the vector field F = (x 2 - y)i + 4zj + x 2k, where the closed…

A: We are given a 3d vector field and a cloced conture, using which we have to justify the Stoke's…

Q: 1) Sketch the vector field F. (i) F(r, y) = (ii) F(r,y, 2) = i

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Q: Determine the vector field of F. F(x, y) = 81-4)

A: The given vector is F=8i-4j

Q: Sketch the vector field of F = (-y,0) in the xy-plane. %3D

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Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Calculate the flux of the vector field F(x, y, z) = (3x + 5) through a disk of radius 4 centered at…

A: we use the formula Flux=∮F.ndS to calculate the flux.

Q: Calculate the flux of the vector field F(x, y, z) = (5x + 9)ỉ through a disk of radius 3 centered at…

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Q: Sketch the vector field F(x, y) = (-x − y, x - y) at the points (x, y) where x, y = {−1,0,1}.

A: Consider the given vector field, F→x,y=-x-y,x-y Here we need to sketch the vector field at the point…

Q: Determine the vector field of F. F(x, y) = 9i - 3j y y

A: We will determine the vector field graph for given vector field using ve tor field plotter.

Q: Calculate the work done by the force: F(x, y, z) = (y — z)î + (z + x)ĵ+ (x + y)k in moving a…

A: Given: F→x,y,z=y-zi→+z+xj→+x+yk→ and r→t=2cost, 2sint, 2sint; t∈0,2π We have to calculate the work…