Which of the below graphs is of the following vector field? F(x, y) = xi + yj

Q: Make a sketch of the following vector field. F= (2y.x)

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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: Is the vector field F(x, y) = 2xy+y 2xy+ xy+y*x x conservative? Select the correct answer below: O…

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Q: Consider the vector field F = (5x + 6y, 6x + 4y). F - dr along the curve C given by r (t) = (t², t*)…

A: ∫CF→·dr→=∫abF(r(t)) r'(t) dr

Q: Q4: Find the curl of the vector field F(x, y.2) = x*/yi +j+ zk at the point(2,4).

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Q: Find the divergence of the vector field F. F(x, y) = 3xe*i - 9x²y²j

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Q: What is the value of a so that the vector field F(x.y)=(In y+2xy³) i+(ax²y2+ x/y) j is conservative?…

A: To find: the value of a for which given vector field is conservative.

Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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Q: How much work is required to move an object in the vector field F= 5 y2i + 2xy J  Along the curve ,…

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Q: Which one of the following is a potential function of the following vector field? O f(x,y) = xy+2x O…

A: Find potential function

Q: Is the vector field F = y? – 2x², 2xy + 3| conserva Yes No yz Is the vector field F y? – x2 con Vy?…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: (2) For a differentiable vector field f, which of the following is (are) incorrect? (a) ▼ × (▼ × ƒ)…

A: Since we know Formula a→×(b→×c→)=(a→·c→)b→-(a→·b→)c→

Q: Given the following vector field and orientated curve C, evaluate F•Tds. (x,y) F = (x² + y²) on the…

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Q: The figure to the right shows a plot of a vector field F along with three curves, C1, C2, and C3.…

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Q: Find the curl of the following vector field: F = (z, 2y, -3x)

A: Follow the procedure given below.

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 6x²y²j

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Q: Graph the vector field  F(x,y)=(x-y)i+xj

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Q: Which vector field would generate this graph? 0( - y, – a) O (y, z) O (x, – y) 0( - 1, y)

A: We check the given vector field one by one. First one is fx,y=-y,-x Now, for point 1,1 we see that…

Q: a) Find the curl and the divergence of the vector field: F = (3x + 2z?)i + (*)j- (2- 7x)R.

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Q: Make a sketch of the following vector field. F = (-x,2y) %3D

A: We sketch the vector field, we choose  the  points and sketch them.

Q: Which of the following vector field is not conservative? a) Å(r, y) = yi- 3ryj b) 72r + 14(x² +…

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Q: Make a sketch of the following vector field. F= (2y, - x) Choose the correct vector field below. O…

A: The given vector field is F=<2y,-x>

Q: 14. Find the curl of the vector field F = x²i – xevj+ 2xyzk

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Q: Find the divergence of the vector field F. F(x, y) = 7xe*i - 4x²y²j

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Q: F(x.y) = (4xy, - 3y²> A V.F- 4x B VF-1 © v.F = 4x - 6y (D vi--2y

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Q: Make a sketch of the following vector field. F= (e -X,0) Choose the correct vector field below. OA.…

A: If you like the solution then please give it a thumbs up.... The Answer is:    Option (c) will be…

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

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Q: Find the divergence of the vector field F. F(x, y) = 7XEX¡ – 9x²y2j

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Q: Determine the vector field of F. F(x, y) = yi – xj 1 1

A: We need to determine the vector field of Fx,y=y i^-xj^    x,y Fx,y=y i^-xj^ =y,-x 1,0 0,-1…

Q: 4. Show, in detail, that any vector field of the form (*,J, 2) = J (*) +8(y)/+h(z)k is irrotational,…

A: To show that the vector field is irrotational.

Q: 1 Find the divergence of the vector field F -(xi + yj+ zk) Vx? +y? +Z 2 x² + y² + z? 1 x² + y? + z?…

A: If the vector field is given by F=F1i+F2j+F3k then the divergence of F is ∇·F=∂F1∂x+∂F2∂y+∂F3∂z.

Q: Evaluate both sides for the field- rectangular parallelepiped X = 0 and 1 Y=0 and 2 and Z=0 and 3.…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 山供 得 三 -5+ 5 X 三 -5+ ||| 三 5 BE 州 X x

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Q: If F is a vector field, then | É.d7 = F(B) – F(A) where the curve C goes from A to B.

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Q: Find the divergence of the following vector field. (x.y.z) F= 6+ 4x + 3y 2 The divergence of F is

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Q: Find a potential function for the vector field F by inspection. (If an answer does not exist, enter…

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Q: Select the correct vector diagram for the given vector field: E = xr - yy

A: We are given the vector field : E=x^x-y^y Plotting the vector field we have: Now, if we observe the…

Q: Consider the vector field F(x, y) = (x², −y). If (x, y) is in the first quadrant then the vector…

A: Part 1. (x, y) is in the first quadrant.  => x > 0 and y > 0 => x2 > 0 and - y < 0…

Q: Which of the following is the divergence of the vector field F=x,y,z)? none of these 3. -3

A: The correct option is 3rd option .i.e. 3 .

Q: Find the divergence of the vector field F div F II

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Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 5x2y²j

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Q: 3. For Parts (a) (b), does the given vector field F appear to be conservative? Clearly answer yes or…

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Q: Match the vector field with its graph. F(x, y) = yi 臺 -6+ + HH H + 三

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Q: Q5. (a) Show that the curl of F is the vector field VxF=i-j-k

A: answer is in next step . please give a like .

Q: Given the vector field F(x,y) = [x/((x^+y^2)^(3/2)), y/((x^+y^2)^(3/2))], Find a fucntion f(x,y)…

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Q: Compute the curl of the following vector field. F= (x? - y°,5xy,2z) The curl of F is (Oi+ (Di+(k.

A: Topic- vector calculus

Q: Find the divergence of the vector field F. F(x, y) = 3x?i + 4y²j

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Q: 25. Evaluate |F•T ds for the vector field F = x²i – yj along the curve x = y? from (4, 2) to (1,–1).

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Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: