Let F(z, y) be the vector field plotted below, and let C be the piecewise-linear path from (8, –5) to (8, 5) to (10,5). What is the sign of F - dr? 10 -10 -10 10 Select one: O a. positive O b. negative O c. zero

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

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Q: What is the divergence of the vector field f=3x i+5xy j+xyz'k at the point (1, 2, 3). Select one: а.…

A: Solution:-The given vector  field is Step:-1    f=3x2i+5xy2j∧+xyz2k∧  then,  we have  to find the…

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: What is the value of a so that the vector field F(x,y)=[y eX+4xy3) i+(ax3y4+ e%)j is conservative? О…

A: We are asked to find the value of a.

Q: 4. consider F(x, y) = (y² − 2xy) i + (2xy − x²) j. (a) Show that F is a conservative vector field in…

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Q: Q3 Given the conservative vector field, F =(x +y²)i +(2xy +5)j , evaluate the integral F•ds where C…

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Q: Find the curl of the vector field F. F(x, y, z) = 4x² + 7y²j + 5x²k

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Q: The divergence of a vector field F(x,y, z) = (x + y)i+ (y + z*)j + (x + z“)k at the point (1,1, 1)…

A: The divergence of a vector field is a scalar quantity that can be computed by computing the dot…

Q: e) Find the divergence of the vector field at the given point: F (r, y, 2) = In (æyz) (i +j + k);…

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

A: Given vector field and point now we have to find curl F as shown below

Q: Match the vector field to its graph. 1. 2. = %3D 3. F (x, y) 1 = F (x, y) = F (x, y) 4. E 5.

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Q: Given the 2-D vector field : G(x, y) = (2y)î + (x)j and the triangular curve T : line segments from…

A: Given: G→x,y=2yi^+xj^ Triangular curve T, line segments from point A0,0 to point B4,0 to point D4,2…

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: Consider again the vector field F = (x +y)i + (x² + y²)j_what is the downward flux across the line…

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Q: 2. Determine if the vector field, F = (2ry- 22)i+(r² + 2z)j+ (2y-2rz)k, is conserva- tive. If the…

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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: Find the curl and divergence of the vector field. F(x,y,z)=x^2yz i -x x^3y k

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

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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: Determine and state the work done by the vector field over the given path in situation. F (x,y) = (x…

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Q: 4) Determine whether the vector field hlxiy)= y?i+ 12xy-e4)T is conservative conservative, deter…

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Q: At how many points is the vector field F(x, y, z) = (z– ,r – 2², y – x²) irrotational? Select one:…

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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: 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: Consider the vector field v(z) = i+ i+4k . a) Calculate fu• dr , where l' is the straight line from…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

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: 4. Determine whether or not the vector field F(x, Y, z) = (-xye®, -xe + e° + 2y, 2z) is…

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Q: Q4. A vector field F is defined as F = psin pa,+ 2p² zas + zcos oa,. The V × F at point P(1, 7/2, 2)…

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Q: How much work is required to move an object in the vector field F = 5 y² ỉ + 2xy] Along the curve C,…

A: Given: F=5y2i+2xyj  C1 is the line y=0 C2 is the line x=1 C3 is the line segment joining points 1,1…

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: 9) Find the (i) divergence and (ii) curl of the vector field F(2, y, 2) = (4yz) i+ (y²z) j + (ryz) k

A: We have to find curl

Q: determine if the given vector field f is conservative and hence find the potential function for the…

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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: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: Q4/ if r(x,y, z) = xi + yj + zk be the position vector field on R3. Find The Laplacian of ||r||?

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Q: A vector field is given by F = (2y + 3)i + xz j + ( yz -x)k, evaluate ∫ ?. ?? c

A: Given: F→=(2y+3)i⏞+xzj⏞+(yz-x)k⏞ C is the curve given by r→(t)=2ti⏞+tj⏞+t3k⏞ where t varies from a=0…

Q: 2. Sketch the vector field F(x, y, z) = xi + yj + zk.

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Q: 9. (~Ch16 Review #13) Find the work done by the conservative vector field F(x, y) = along the curve…

A: given a conservative vector field  Fx,y=4x3y2-2xy3,2x4y-3x2y2+4y3 and a curve  rt=t+sinπt,2t+cosπt…

Q: 9. Find the flux of the vector field B(x, y,=) shown in the left figure through the square S of - yỉ…

A: The general form of a vector valued function in three dimensions is given by…

Q: Let F : R³ → R³ be the vector field defined by F(x, y, z) = (2xy + z², 2yz + x², 2xz + y² Prove that…

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Q: What is the value of a so that the vector field F(xy)=(In y+2xy³) i+(ax3y2+ x/y) j is conservative?…

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Q: G is a vector field defined as G = Bxlnzi + Dy²zj + (E+ y³) k. a) Find the values of B and D for…

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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: Determine and state the work done by the vector field over the given path in situation. a. i. F (x,…

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Q: The vector field F(r, y) = (2xy +y) dx + (æ + 2xy) dy is conservative. %3D The function f(x, y) = x²…

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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: Evaluate ∫C F . T ds for the vector field F = x2 i - y j along the curve x = y2 from (4, 2) to (1,…

A: Given information: The value of F=x2i+yj, x=y2 and from (4, 2) to (1, -1). Calculation: Consider…