xi + yj F(x, y) = k- x² + y2'

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

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Q: Find the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y).   Enter the exact…

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

A: Solve for the gradient vector

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

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x2zi – 2xzj + yzk; (9, -9, 5)

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and…

A: Solution: The objective is to find a vector tangent to the curve of intersection of the two…

Q: Look at the vector field in the plane F. Xi - j

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 3| for fluid flowing…

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Q: Determine the vector field of F. F(x, y) 3D yi — хј

A: Let us make a table to draw the vector field as shown in the image below.

Q: Find the work done by the vector field F = in moving a particle around the circle x2 +y2 = 4 from…

A: The given vector field is F=x-y, xy. The particle is moving around the circle x2+y2=4 from 2,0 to…

Q: Find the conservative vector field for the potential function by finding its gradient. (x, у, 2) %3…

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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 gradient vector field of f бу f(x, у, 2) = X COS Z (бху) (6y бу -sin бх -sin бу i cos k…

A: Given,

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

A: This question is from vectors.

Q: Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.

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Q: Find the flux of the vector field F = (x, z, - y) through the helicoid with parameterization r(u, v)…

A: Given :-  The flux of the vector field  F→ =  x3 , z , -y through the helicoid with the…

Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

A:

Q: Find the gradient vector field of f(x, y) = x°y*

A: Given,          The gradient vector field of fx,y=x5y4.We know that,          The gradient vector…

Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 5 for fluid flowing…

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Q: 1. Verify the Divergence Theorem in the calculation of the flux of the vector field: through the…

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

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Q: Find curl F for the vector field at the point (9, -9, 5). F(x,y,z) = x²zi - 2xzj + yzk curl F =

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

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Q: Why is the upward flux of a vertical vector field F = ⟨0, 0, 1⟩ across a surface equal to the area…

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Q: disk

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Q: Find curl F for the vector field at the point (3, -9, 1). F(x,y,z) = x2zi - 2xzj + yzk curl F %3D

A: Given: The vector field is F(x,y,z)=x2zi^-2xzj^+yzk^ The objective is to find the curl F of the…

Q: Find potential 9, for the conservati ve field the vector F (x, y,a)- (2xe? - y*sinx) î * sinx) î +…

A:

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: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: Given: f(x, y, z) = 9x2 − xy − z2

Q: . Verify Stoke's theorem for the vector field F = (2x - y) I– yz²J -y z K over the upper half…

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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: Let be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny).

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

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: Given : f(x,y,z)=9x2y+5z2   To Find : Conservative Vector field by finding it's gradient

Q: Sketch the vector field F(x,y)=1/2xi-1/2yj at points (-1,1),…

A: Put each given points in F and find subsequent coefficients of vector F to find (x1, y1) Plot the…

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y,…

A:

Q: Calculate the flux of the vector field F 6i + 2x2j- 2k, through the square of side 4 in the plane y…

A: Given vector field is F→=6i→+2x2j→−2k→ We have to find the flux of the given vector field. The flux…

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (9, -9, 7)

A: The curl of a vector field F is defined as  ∇×F=i^j^k^∂∂x∂∂y∂∂zf1f2f3

Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) = x² sin(3yz) F(z, y, 2) = (

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Q: Compute the outward flux of the vector field F = (5xy, 5y²) for the region enclosed by the curves y…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Calculate F=, around the triangle with vertices: (0,0,2), (2,0,0) and (0,2,0). Can you use Stoke's…

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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 the…

A: The objective is to find the flux.

Q: i = e-* sin x

A: Given dxdt=e-xsinx. We equate the RHS of the differential equation above, e-xsinx=0 As e-x≠0, we…

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F…

A: