Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is conservative or not.

Q: How do you graph the vector field F = ⟨ƒ(x, y), g(x, y)⟩?

A: Given: vector field

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: Find the divergence of the vector field F <7", 22°, zy* div F -

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Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: F = (x² +y², y² +z?,.

A: on solving this we get the

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: 10. For a vector field F = <2xy + y³, x² + 3xy²+ 2y7 find a function f such that F = Vr.

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Q: Q4 A) Calculate the divergence of the vector field F=y³i + xyj B) Find the Curl of F(xy.z)=3x²i +…

A: To find out the divergence of vector field.

Q: Calculate the divergence of the vector field F=x²y³z¹i-xyzj+(x+y+z) k

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Q: Find the conservative vector field for the potential function h(x,y,z)=3xyln(x+y) by finding its…

A: Find gradient

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 7x?y²j

A: Find the divergence of the vector field F.

Q: How do you determine whether a vector field in ℝ2 is conservative(has a potential function w such…

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Q: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

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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 conservative vector field for the potential function by finding its F(x, y) = x² + 5y2

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

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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 divergence of the vector field F = div F =

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

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Q: 13

A: We have to find out conservative or not

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

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Q: 5. Suppose that the vector field F = is conservative. Find a potential function of the vector field…

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Q: b) Evaluate both sides of the divergence theorem for the vector field D = 2xyx + x²9 [C/m²] and a…

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Q: (xy³ +3x²y, 3xy² + x²) 2+x ху у,

A: According to question given that Vector Field F⟨xy3+3x2y, 3xy2+x2⟩

Q: Q3) Determine if the vector field F(x, y, z) = (yz,xz + 2y, xy + 1) is conservative. If it is, find…

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Q: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

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Q: Determine whether the vector field F(x, y) = conservative. yi + xj 1 + xy is

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Q: a) Determine whether or not the vector field F 8yz, – 6 cos(y) – 8xz, – 8xy + 10z > - is…

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

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: Find the divergence of the vector field F = < ya", xz°, zy* div F

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Q: What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² – k².

A: If z=f(x,y), then the variables x, y are called the input of the function, and z is called the…

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

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Q: Find the divergence of the vector field F. F(x, y, z) = In( 7x²+ 4y² )i + 28xyj + In( 4y2 + 5z2 )k

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Q: Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² -k².

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

Q: F(x, y) = 6xyi + 3y²j is a conservative vector field.

A: Given :F(x,y)=6xyi+3y2j

Q: b) Verify whether the vector field F is conservative, if so, then find the potential function F = ,…

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Q: Find the divergence of the vector field F. F(x, y, z) = In 5x²+ + 10xyj + In( 2y2 + 722)k div F(x,…

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Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

Q: 3. Use the divergence of the vector field to compute F(x, y) = (tan-1 (2x)) ₁ + (xy-2 +²8²) J j 4 fo…

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Q: The divergence of a vector field F = 3x² yz? î + 2yz ĵ – xz² k at he point (1,0, 1) is -2 O 2 O 1

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

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Q: Q5: Find the divergence of the vector field y F(x, y, z) = x² √yi + =j+zk At the point (2,4,1).

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Q: Q3 Show that the vector field F= 2xyi +(x -2y)j is conservative and evaluate the line integral |F•ds…

A: Solution

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: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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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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