Show that F of F. = (2xy + z³)i+x²+3xz²k is conservative force field. Find the scalar potential

Q: 2. Sketch at least ten arrows in the vector field: F(x,y)=(-2y)i + (x+1)j

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Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: We have to find the rate of heat flow out of a sphere of radius .

Q: Determine whether the vector field F(x,y,z)=(y,x,1) is conservative on R° . If so, determine a…

A: Given the vector field Fx,y,z=y,x,1=yi→+xj→+k→.

Q: Q4 A) Calculate the divergence of the vector field F=y³i + xyj B) Find the Curl of F(xy.z)=3x²i +…

A: To find out the divergence of vector field.

Q: Find the directional derivative of the scalar field = xy + 4xz at the point (2, -2, 4) along the…

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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: Sketch and describe the vector field F (x, y) = (-y,2x)

A: The given vector field is F→x,y=-y,2x A vector field F→ in ℝ2 or ℝ3 is an assignment of a…

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: Since the surface is whole sphere, that is S is closed so we can apply Gauss Divergence Theorem.

Q: A) Consider the vector-field F(x, y) = 2xy³i+ 3y²x²j. 1. Show that F is conservative. 2. Find a…

A: The given vector field is  F⇀(x,y)=2xy3i⇀+3y2x2j→ We have to show that F→ is conservative

Q: Compute the flux of the vector field F =2xi +3yj through the cylindrical surface shown below, if a=3…

A: Given that the vector field is F(x,y)=2xi+3yj Let us parametrize the cylinder as x=cosθ, y=sinθ, z=r…

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: 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: The gradient of f(x, y) = x sin (y²) is the vector field F (x, y) = at (2,√π/6) and ending at…

A: Here we are given that the gradient of f(x,y)=xsin(y2) is the vector field F(x,y)=sin(y2)2xycos(y2)

Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

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

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Q: ed by F(x, y) = (-: %3D

A: The function given is , F→x,y=-x,y. Draw the table for the points plot on the graph for the vector…

Q: Find the curl of the vector field u = a) b) ▼xu =( V. (V x u) = = (7xyz², 6x² y³, 2x³ y³ z4 ).

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Q: let 2 Vector tield A=x B=y2 Find explicit expresom of Lie derivative L, CB)

A: Please find the answer in next step.

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: For the vector field (x³z², o, -x²z), evaluate the line integral on the clase curve made by a square…

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Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

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Q: Compute the flux of the vector field - 5yi + 3j- 5azk through the surface S, which is the surface y…

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Q: 5) Integrate the vector field h a,y)= y2i+ (2xy-e*)J C parumetrizal by t€ £0, 5 3. over the circular…

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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…