Consider the vector field F(x, y,z)= 2.xy i+(x² +z? ) j+2yzk . c) Is F a conservative vector field? If so, find the potential function of F. d) Let C be the curve that moves along the line segments from (1,1,0) to (3,1,0) then from (3,1,0) to (3,4,2). Find [F•dr

Q: Compute the upward flux of the vector field Ĥ(x, y, z) = (x, 0, 2z) across the portion of the…

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Q: Compute the curl and divergence of the vector field F(x, y, z) = (T 2², 2yz) . Is F conservative? If…

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Q: Use the divergence theorem to find the outward flux of the vector field F(x, y, z) = 4x²i + 5y²j +…

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

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Q: Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, –6z – 32²y²)…

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz2j + 4yz²k; (5,…

A: Recall divergence is a scalar and has formula enclosed in next page

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Q: Which of the following functions is a potential function for the conservative vector field F(x, y,…

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Q: Find the work done by vector field F(x, y, z) = xi + yj + (x + z)k on a particle moving along a line…

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Q: For the vector field F(x,y,z)=ya'1+x1+2xyz k a) show that F is conservative vector field; b) find a…

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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: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

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Q: Consider the vector field F(x, y, z) = (2xy, x², 1). (a) By calculating the curl of F, show that F…

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Q: Find the potential function p, for the conservative vector field F(x, y, z) = (2xe² – y²sin x)î +…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z)=-3ry-ly:j-Szak…

A: To find- Use the divergence theorem to calculate the flux of the vector field F→x, y, z = -3xyi^ -…

Q: Let F be the vector field F(r, y, ) = =i- sin yj+ (2r: +6:)k. Compute divergence and gradient of the…

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

A: The given vector field is, F→=y, -z,  x. The given part of the plane is z=4+2x+3y And the rectangle…

Q: Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=3x2i+1y2j+2z2k…

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Q: Determine whether F(x, y) = xi +9yj is a conservative vector field. If so, find a potential function…

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Q: Find the flux of the vector field F(x, y, z) = (y z, y, æz) across the surface S, where S is the…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(4x + y + 62) . F(1, y, 2) =

A: we have to find the gradient vector field of f

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F across the boundary…

A: Given The given vector field is F=3z+x,7x-9y,y+5z Region between the spheres of radius 1 and 4.

Q: Determine whether the vector field…

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Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

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Q: Verify that the vector field f is conservative and find its scalar potential. 3r f = + yz + 2xz) i+…

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

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A: We apply formula for finding this

Q: Consider the vector field F (x, y, z) = (2e2" cos(3y), –3e2" sin(3y) +VV?) Y y' 2 COS a. Find…

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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: A conservative vector field is given as F = 6xe'i + (3x²e" –10yz')j-15y²z°k. Find the potential…

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

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Given that the vector field F(x, y) = (2x-3y, 2y-3x) is conservative in the xy-plane. If (x, y) is a…

A: We have to find the value

Q: Given the vector field F (x, y, z) = 2xyi + (x² + z?) j +2yzk a. Verify that the vector field…

A: Ans :A)

Q: (a) Show that the vector field F(x, y, z) = (1 + 3x²y)i + x³j is conservative and find the potential…

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

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Determine if the vector field F(x,y,z)= (yz,xz+2y,xy+1) is conservative. If it is, find its…

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Q: Determine whether F(x, y) = e cos 9y i – e" sin 9yj is a conservative vector field. If so, find a…

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Q: Show that the vector field F = 2.xyi +(x² – 2 y)j is conservative and evaluate the line integral…

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: Compute the flux of the vector field F(x,y,z)=5xj+2yk→through the surface S, where S is the part of…

A: Flux problem...

Q: Suppose a vector field F(r, y) = construct a potential function o(r, y). i+ j is conservative. Then

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Q: Compute the flux of the vector field F = zi + 8xj through the parameterized surface S oriented…

A: We have find the flux of the given vector field through the parameterized surface S oriented upward.

Q: Suppose a vector field F(x, y) = wai + VEj is conservative. Then construct a potential function ø(x,…

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Q: Determine whether the vector field…

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Q: B) Find the work done by the conservative vector field F (x, y, z) = yzi+xzj+xyk along a smooth…

A: Since, it is given that the field is conservative.

Q: Let C be the helix that winds around the cylinder x2+y? = 1 (counterclockwise viewed from the…

A: here i used parametric equation of helix and done simple calculation like dot product and after that…

Q: 3. Determine if the vector field F(x, y, z) = e" sin yzi + ze² cos yzj + ye² cos yzk is conservative…

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Q: Calculate the vector field flow f➝ (x,y,z) = (xy, y2, z) through the outer surface of solid T in the…

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Q: Find the potential function p, for the conservative vector field F(x, y, z) = (2xe? – y²sin x)î +…

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