Compute the flux of the vector field (x3, – xy³), - out of the rectangle with vertices (0,0), (3,0), (3,2), and (0,2) 6

Q: Compute the circulation of the vector field F=(4cos(y))i+(3x^2sin(y))j around C. Where C is the…

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Q: Assume that Ax, y, z) is a vector field whose i component is only in terms of y and z, whose j…

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Q: Compute the flux of the vector field F(x, Y, z) = 6i + 5j + 3k through the rectangular region with…

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Q: Match the vector field with its graph. F(x, y) = yi -6+ 世 -5+

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Q: Vector fields V and W are defined by V- (2х — Зу + z, -3х — у + 4z,4y + z) W- (2x - 4y — 5z, - 4x +…

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Q: Compute and sketch the vector assigned to the points P = (0, 1, 1) and Q = (2, 1, 0) by the vector…

A: Solution:Given       P = (0, 1, 1) and Q = (2, 1, 0)F=<xy,z2,x>To sketch the graph of F

Q: 2 line of the following vector field that passes through the specified point z²k; (2, 1, 3)

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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: Compute the outward flux of the vector field

A: Given,         F(x, y, z)=x3i+y3j+z3k And S is the surface of the solid bounded by the cone…

Q: Explain how to compute the curl of the vector field F = ⟨ƒ, g, h⟩.

A: Here given

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: A smooth vector field F has div F(2, 5, 5) = 2. Estimate the flux of F out of a small sphere of…

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

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Q: Compute the curl of the vector field F⃗ =7zi⃗ +6yj⃗ +4xk⃗

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Q: Compute the flux of the vector field (x, - xy*), out of the rectangle with vertices (0,0), (5,0),…

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

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Q: Determine if the vector field F=(yz,xz,xy) is conservative?

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Q: Compute the curl, V x F, of the vector field. F(x, y, z) = 7xi + 9yj + 2zk curl(F) = -7xi – 5yj +…

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Q: 3. Let F be the vector field (ze²z + yz², xz², xe*z + 2xyz)

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Q: Compute the flux of the vector field (x2, - xy*), out of the rectangle with vertices (0,0), (4,0),…

A: Given,

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: What does it mean to say that a vector field is conservative?

A: What does it mean to say that a vector field is conservative?

Q: What are the outputs of a vector field in ℝ3?

A: What are the outputs of a vector field in ℝ3.

Q: Provide two examples of physical phenomena in which the divergence of a vector field is nonzero.

A: Q: What is Divergence? A:  It operates on vector field (having magnitude + direction both) , for…

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (7, -9, 5)…

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Q: Find the level surfaces of the scalar field U = ear, where the vectors are: a = (2, 2, 1) and r = =…

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Q: Sketch the vector field. y F(z, y) = (-2 | 2 -2 -2 2 -2 2 -2 -2 -2 4+ -4 -3 -2 -1 3 -1 -2- -3 -4…

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Q: Let divF(x, y, z) = 4x³ + 4y3 +4z³, where F represents the flow of a vector field. Estimate the flux…

A: Given divF→x,y,z=4x3+4y3+4z3radius r=0.1 Centered at point 1,1,1

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

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Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

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Q: Find the gradient vector field of flx, y, z)=x'y+y%z4+xz6 O V flx, y,z)= (3x?y+z°, 5x³y³ + 4y*zA,…

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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: A smooth vector field F has div F(5, 2, 5) = 2. Estimate the flux of F out of a small sphere of…

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Q: Let F(x,y,z)=(2xz^2,−2xyz,9xy^3z) be a vector field and f(x,y,z)=x^3y^2z (∇f=(  ,  , )). (∇×F=(  ,…

A: Given:F(x,y,z)=2xz2,-2xyz,9xy3zf(x,y,z)=x3y2z

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 curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (3, -9, 7)…

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Q: Match the vector field with its graph. F(x, y) = yi y 1信 5 5 y 5 -6+ -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, 7)

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

Q: A smooth vector field F has div F(1,4, 4) = 7. Estimate the flux of F out of a small sphere of…

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Q: Let divF(x, y, z) 4x3 + 4y3 + 4z³ , where F represents the flow of a vector field. Estimate the flux…

A: Given that a small sphere of radius 0.1, centered at the point  (1, 1, 1).And                  div F…

Q: 6. Show that the system with vector field -x + sin(y) F(x, y) : -y+ cos(x), admits no periodic…

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Q: Find the gradieat of the functionf = xyz-4y2z. Visualize the vector field of the gradient. %3D

A: In vector calculus, the gradient of scalar valued function denotes the direction in which the…

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: Find the curl of the vector field at the given point. F(x, y, z) = x2zi − 2xzj + yzk; (9, −9, 1)…

A: Given function is F(x, y, z) = x^2zi − 2xzj + yzk; We find curl F at (9, −9, 1)

Q: Find the gradient vector field of f(х, у, 2) — е6х + 3у +2:

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Q: Find the flux of the vector field F(x, y, z) = [x4, −4yx3, 7z + sin(xey))] through the outwards…

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