Let v= [x-2y, x+2y², z] be a vector field. 1- Compute Curl(v). 2- Find the condition on x, y, and z such that v is irrotational.

Q: If the vector field v = [mz+x, -y, x]is irrotational, the mis equal to O A. 2 O B. 0 O C. 1 O D.…

A: Curl of v is zero.

Q: 1) Consider the vector field F(x, y,z)= 2xyi+(x² +z² )j+2 yz k . a) Find div(F(0,2,3)) b) Find curl…

A: topic - divergence and curl of a vector a) 8  b) 0

Q: Consider the vector field Ĥ(x, y, z) = (y², x, z²). Let S3 be the portion of the paraboloid 2 = x² +…

A: Please comment if you need any clarification. if you find my answer useful please put thumbs up.…

Q: Find the curl of the vector field F. F(x, y, z) = (2y - z)i + e²j + xyzk

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Q: Given a vector field F = 5(x² + y²)i+ 2xyj - 3zk, evaluate SSS, V· FdV for which the solid D is…

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Q: 2) For the vector field F(x, y, z)=(xz²-x²y)i + (xy²-y³2²)] +xy²z³k, find the following: a) Find the…

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Q: Consider the vector field F(x, y, z) = (2xy, x², 1). (a) By calculating the curl of F, show that F…

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Q: Compute the curl of the following vector field. (x, y, z) 5/2 F= (* +y? +z?)* The curl of F is (Di+

A: On solving this problem we will get

Q: Let v = [x2-y?, x2 +y², z] be a vector field. 1- Compute Curl(v).

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Q: Consider the given vector field. 8 F(x, у, 2) %3D (x i + y j + z k) x² + y2 + z2 (a) Find the curl…

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Q: Compute the curl of the following vector field. F= (x? - 4y² ,3xy,3z) The curl of F is Di+( Di+( Dk.

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Q: Let F(x,y) = (ax?y +y³ + 1)i + (2x³ + Bxy² + 2)j be a vector field, where a and ß are constants.…

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Q: 1. Check if the provided Vector Field is conservative or not, write down the formulation of the…

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Q: Compute the line integral of the vector field F = (3zy-¹, 4x, -y) over the path c(t) = (e¹, e¹, t)…

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Q: 2. Show that any vector field of the form F(r, y, z) = f(y, z)i + g(x, z)j+ h(x, y)k is…

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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: A vector field is given as G = (1/(√x² + xy))(e¯²ax +xzay), find the unit vector which is normal to…

A: The given vector fields are: G=1x2+xye-zax+xzayP=3x2ax-4yay We have to find the unit vector which is…

Q: Let v = [x2-2y², x²+2y², z] be a vector field. 1-Compute Curl(v). 2- Find the condition on x, y, and…

A: Curl of a vector.

Q: (7) Find (a) the curl and (b)the divergence of the vector field. F (x, y, z) = xye' i_± yze*k

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Q: Given the vector field F(7, y, 2) F (x, y, z) = compute the curl of F and find the values of a and…

A: curl(F)

Q: xi + yj x2 + y2' F(x, y) = k

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Q: 3) Find the curl of the vector field F(r, y, z) = (ry") i + (ya)j+ (8ry) k %3D

A: We know,If, F(x,y,z)=Fx i +Fy j+Fz kCurl of  F(x,y,z)=∇× F(x,y,z)=ijk∂∂x∂∂y∂∂zFxFyFz

Q: Is the vector field F (x, y) = (2xy – y³) î + (x² – 3xy²) ĵ solenoidal, conservative, both or…

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Q: Use Green’s Theorem to compute ʃC F dr where the vector field is given by F (x, y) =< 3y, xy >…

A: Given:F (x ,y ) = (3y,xy)  and C is the square with vertices (3,0), (3,5),(-1,5) and (-1,0) oriented…

Q: What is the curl of the vector field F(z, y, z) = ryi+ zyzj + yzk O a. (-ry + z)i + (yz – 2)k O b.…

A: We have to find

Q: 5. Find the curl of the following vector field in both Cartesian and cylindrical coordinates. F=…

A: Curl of a vector field represents the circular nature of vector field. Curl of vector field F=a,b,c…

Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

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Q: Let Σ be the sphere x2`y2`z2 “ 25 with outward orientation and let F~ be a vector field with divF~ “…

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Q: 1. Consider the function f (x, y, z) = y- + y² +z? Determine the gradient vector field of f, F =Vf…

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Q: d) Determine whether the vector field is conservative. If it is, find a potential function for the…

A: Let a vector field is given by,                                  The vector field is conservative…

Q: In a vector field V = (y^a,−x^b,z^c) what is the value of the z-component of curl (V) at (x, y, z) =…

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Q: Let 8. (x2 + y²)%, F = xyz x² + 17 be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}. Find…

A: Given F=8x2+y2, x2+y252, xyz17 is a vector field on U=x, y, z∈ℝ3 | x, y≠0, 0 We will find its curl…

Q: Let v = [x2-2y, x² +2y², z] be a vector field. 1- Compute Curl(v).

A: Since you have asked multiple questions in single request.so we will answering only first question.

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

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Q: onsider the vector field F(x, y, z) = ( 2, -3, x*), and the rectangle R = {(x, y, 0)| -1<x< 1, -1 <…

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Q: Consider the vector field i = P(x, y) = –3y+ ¤(x² + y² – 1), ý = Q(x, y) = 3x +y(x² + y² – 1) | %3D

A: consider the following

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.  =&gt; x &gt; 0 and y &gt; 0 =&gt; x2 &gt; 0 and - y &lt; 0…

Q: 4. Find the curl of the vector field F = %3D curl F = k

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Q: ) Show that the vector field, F3 yz £ + zx ŷ + xy 2 c

A: Given: The vector field is, F3 = yz x^ + zx y^ + xy z^

Q: Determine if the vector field F = y ln zi – x ln zj + xyk is a conservative vector field.

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Q: Verify Green 's theorem for the vector field  F (x, y) = (x^2y, -xy^2) in the triangle OAB defined…

A: The solution  is given by using the line integral of vector field and verify the greens theorem as…

Q: Compute the curl of the vector field F = -2z i – 3y j – 5x k.

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: Consider the vector field F(z, y. 2) = -3yzi +(-3rz +2yz²)j+ (-3zy+ 2y°z + 1)k. (a) Calculate curl F…

A: Note: As in the part (B) the page 94 is missing, so we are solving one (a) part of the given…

Q: Compute the curl of the following vector field. F = (3xz° ev? 2xz° ey, 3xz? eY*) %3D The curl of F…

A: The given vector field is F=3xz3ey2,2xz3ey2,3xz2ey2.

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: 2. Use Gauss's theorem to evaluate DEa$ for the vector field, Ę =, taking S to be a portion of the…

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Q: Let v = [x²-2y², x²+2y2, z] be a vector field. 1-Compute Curl(v). 2-Find the condition on X, y, and…

A: If curl zero then irrotational

Q: Show that any vector field of the form F(r, y, z) = f(x)i+ g(y)j+ h(z)k is irrotational.

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Q: Let F(x,y)= (a²+1)yi+ (2a)xj. Find a value of a so that the vector field F is conservative. Select…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.