Consider the vector field v(z) = i+ i+4k . a) Calculate fu• dr , where l' is the straight line from (4,0, 4) to (0, 6, 6) .

Q: Sketch the vector field F = ⟨x, y⟩ .

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Q: The gradient vector field of for,y)= In +2y) is 2. T True A False

A: The gradient vector field of a function, is defined by the formula below. , where are the partial…

Q: Sketch the following gradient vector field, F(x, y, z) = 2xi - 2yj – 2xk. Then find the vector…

A: The given problem is to sketch the given vector field and also to find the gradient of the given…

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

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Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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Q: When is the vector field continuous?

A: given,       Continuous vector field .

Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

Q: Find llFll and sketch several representative vectors in the vector field.

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Q: F = (x² +y², y² +z?,.

A: on solving this we get the

Q: Is the vector field F(x, y) = (In y + sin(e²“), #

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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: Compute the curl of the vector field F = - (x + 3y) i + (y – 3z) } – (z + 3x) k curl

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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: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

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Q: Determine if the vector field F(x,y)= (x+y,x−y) is conservative? If it is, find its potential.

A: Given Data The vector field is: F(x,y)=(x+y,x-y).   Write the vector field in standard form, The…

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

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Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

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Q: 2. Show that V(V × F) = 0, here vector field is twice differentiable. %3D

A: This question is from vectors.

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: Write a formula for a two-dimensional vector field which has all vectors of length 1 and is…

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Q: for the vector field F = 2xz i+ (1 – 4xy² ) j led by the plane z = 6 – 2x² – 2y² and the plane

A: We have to find the following conditions according to the given information

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

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Q: Sketch the vector field.  F(x, y) =〈y, 1〉

A: The vector field: F(x,y)=<y,1>

Q: Explain why the vector field ∇(xy + xz - yz) is conservative.

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Q: For the vector field F = ((y/z2+1)i + (-2x/z2+1)j + (3x2+3y2/(z2+1)2)k , calculate curlF

A: We have given vector field F=yz2+1i+1-2xz2j+3x2+3y2z2+12k=yz2+1,1-2xz2,3x2+3y2z2+12=F1,F2,F3…

Q: etch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line segment…

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Q: Calculate the work done by the vector field F(x, y)= ,2xy) on a particle that moves once around the…

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Q: Find the equations of the field lines for the vector field defined by the two dimensional field, F =…

A: Given vector field F=xi^-yj^....(1) Compare the equation (1) with F=dxdti^+dydtj^, we get  dxdt=x…

Q: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

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Q: Compute the flux of the vector field F = across sphere a? + y² + z² = 9.

A: Let F be a vector field and S be the boundary of the surface D. To find the flux of the vector…

Q: compute dr for the vector field where Cis the line segment from Co.o) to Cli3)

A: Given vector field is, F=1+x2,xy2  The objective is to compute ∫CF·dr, where C is the line segment…

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

A: If the vector field f:ℝ3→ℝ3 is continuously differentiable in a simply connected domain  and curl…

Q: Compute the flux of the vector field F = 5xi + yj through the cylindrical surface shown below, if a…

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Q: Calculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to…

A: To find the line vector of following vector fieldF→=-3i+2jalong the line 4,0 and 12, 0

Q: Compute the work done by the vector field F(x, y) = (ry, x² + y³) when moving a particle…

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Q: Find the curl of the vector field F=(2xyz, -xy,-z^2)

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Q: Calculate the line integral of the vector field F = -2i+ 4jalong the line from the point (3,0) to…

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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: F=x²y³z¹i-xyzj+(x+y+z)k

A: The vector field is F→=x2y3z4i^-xyzj^+(x+y+z)k^

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

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Q: Find the curl of the vector field F(x,y,z)

A: The given vector field F(x,y,z)=yex, 2x+3y, ycosx we have to find curl F(x,y,z)=?

Q: Find the gradient vector field of f(x, y) = In(2x + 3y) V

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Q: Compute the curl of the vector field F = 2y3 i+ e j+ cos(x) k curl

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Q: Compute the flux of the vector field F = 2xi + yj through the cylindrical 5 and b = 4 and it is…

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Q: Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

A: Given problem:- Show that the vector field A = (3x²z+ y²)ax + 2xyay + x³az is conservative. =

Q: Calculate the line integral of the vector field F -3 i+ 2j along the line from the point (4, 0) to…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 進 ↑ -6+ <||||||||||| Hex

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