Sketch the vector field F(x, y) = xj, the line segment from (1, 9) to (6,9), and the line segment from (9, 3) to (9, 6). Calculate the line integral of the vector field F along the line segment from (1, 9) to (6,9). Calculate the line integral of the vector field F along the line segment from (9, 3) to (9, 6).

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

A: Given vector field F(x,y,z) =x2 z i -2xz j +yz k   ; (7 , -9 , 5)

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

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Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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Q: Sketch the vector field F(x, y) = xj, the line segment from (6, 1) to (6,5), and the line segment…

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Q: Find the work done by vector field F(x, y, z) = xi + yj + (x + z)k on a particle moving along a line…

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Q: Find the work done by vector field F(x, y, z) = xi + 9xyj - (x + z)k on a particle moving along a…

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Q: Find the divergence of the vector field F(x, y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…

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: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

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Q: Sketch the vector field F(x, y) = xj, the line segment from (1, 4) to (7,4), and the line egment…

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Q: Find the work done by the vector field F = in moving a particle around the circle x2 +y2 = 4 from…

A: The given vector field is F=x-y, xy. The particle is moving around the circle x2+y2=4 from 2,0 to…

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

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Q: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x Y F(x, y) =

A: To find the work done by the force field F in moving an object from P-3, 7 to Q7, 5. Fx,…

Q: Given the vector field v=⟨0,2xz+3y^2,4yz^2 ⟩. Find the line integral of the path from (0,0) to…

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Q: 2. Calculate the directional derivative of the scalar field U(x, y,z) at the point M,, along the…

A: Given that : U=xz3y-x3y=xz3y-x32y12 The gradient will be calculated as :…

Q: Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter…

A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

Q: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

A: The solution are next step

Q: Evaluate the line integral of the vector field (3x2 + 3y + 2xy, 3y2 + 3x + x2) along the curve y = x…

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Q: Explain why the vector field ∇(xy + xz - yz) is conservative.

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Q: Show that the vector field F = x²i + (2yz)j+ y² k is conservative and then find the corresponding…

A: A vector field F is conservative if curl(F)=0 or ∇×F=0 The potential function is given by f such…

Q: Find the work done by the force field F(x, y, z) = on particle that moves along the line segment…

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Q: Compute the line integral of the vector field F = (3zy1, 4z, -y) over the path c(t) = (e*, e', t)…

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Q: etch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line segment…

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Q: A scalar field is given by f = x2/3 + y2/3, where x and y are the Cartesian coordinates. The…

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Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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

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Q: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

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Q: What is the flux of the vector field (x2,y2,z1 ) through a cuboid with x ranging from 0 to 8.3, y…

A: use divergence theorem

Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

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Q: Find the curl of the vector field F(x,y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Let the given vector field is :

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(x + 3y + 4z) . F(2, y, 2) =

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Q: Find the gradient vector field (F(r, Y, 2)) of f(x, y, z) = In(4x + 6y + 22) . F(7, y, 2) = (

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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, 9)

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Q: Show that the following vector field is conservative and find the potential F(r, y, z) = (2ry, x² +…

A: The answer is given as follows.

Q: (2) Find the line integral of the vector field F(x, y) = (-1,3) along the path from (2, 3) to (2,…

A: The vector field F→=-1, 3To find line integral of vector field along the path 2, 3 to 2, 5

Q: Compute the flux of the vector field F(x,y, z) = yi– 2xyk over the triangle T with vertices (1,0,0),…

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Q: Calculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to…

A: To find the line vector of following vector fieldF→=-3i+2jalong the line 4,0 and 12, 0

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: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Calculate the flux of the vector field F 6i + 2x2j- 2k, through the square of side 4 in the plane y…

A: Given vector field is F→=6i→+2x2j→−2k→ We have to find the flux of the given vector field. The flux…

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: Show that the vector field F = 2xyi +(x² - 2y)j is conservative and evaluate the line integral (F•dš…

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Q: Find the divergence of the vector field F = < yx², xz", zy® div F II

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Q: Consider the curve C from (-2, 0, 1) to (6, 5, 2) and the conservative vector field F(x, y, z) =…

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Q: Sketch the vector field F(x, y) = xj, the line segment from (1,9) to (5,9), and the line segment…

A: To solve the following line integral

Q: Calculate the line integral of the vector field F -3 i+ 2j along the line from the point (4, 0) to…

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Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…

Q: Sketch the vector field F(z, y) = i – 2j and calculate the line integral of F along the line segment…

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