Evaluate the work done between point 1 and point 2 for the conservative field F. Here you can assume that the vector field is conservative - no need to check F = 5xi + 5yj + 5zk; P1(4, 1, 4), P2(7, 5, 9) O W = 470 W=0 W = 305 W = - 305

Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

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Q: Find the general solution of the given system. Use a computer system or graphing calculator to…

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Q: Let F(z, y) be the vector field plotted below, and let C be the piecewise-linear path from (8, –5)…

A: Draw the linear path from 8,-5 to 8,5 to 10,5, which is given below.

Q: 13. For the vector fields: A = x + 2y ŷ + 3z 2; B = 3y - 2x ŷ. Check both product rule given in…

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Q: Give three equivalent properties of conservative vector fields.

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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: Sketch the vector field. F(z, y) = (- 2 2 2 0 2 -2 0 -2 2 -2 2 -2 -2 2 -2 4- -4 -3 -2 -1 2 3 -2 -3-…

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Q: (x, y) = x(x + y)

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Q: FTTT 10 5 10- -5- -10- X TTTTI 1C d.

A: We draw the sketch of vector field with the help of direction and length of vectors .

Q: Show that V² (v-x) = 2V.v+x-V²v, where v is a vector field and x is the position vector of a point…

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Q: 6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z,…

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Q: Show that the vector field A and B are everywhere perpendicular if A (2.-5,6) and B (6,5,-2)

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: To Determine: A net is dipped in a river .determine the flow rate of water across the net if the…

Q: Match the vector fields F with the plots labeled I-IV. Give reasons for your choices. F(x,y)= <y,…

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Q: Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

A: Given problem:- Show that the vector field A = (3x²z+ y²)ax + 2xyay + x³az is conservative. =

Q: I need help to directly evaluate S1 by using the vector fields formula as shown below in second…

A: The surface integral of over a surface S: , is given by

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

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Q: If C is the straight line from (1,1,1) to (2,1,2) find 2xlnzdx + 2y²zdy + y³dz.

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Q: How do you determine whether a vector field in ℝ3 is conservative?

A: Suppose, F⇀=Ai^+Bj^+Ck^ be a vector field. So, the vector field is conservative if and only if its…

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 35 호 도로 -5+ 5 € -5+ 5

A: The given vector field is: .To Do:Match the vector field with its graph.

Q: ZX Z ++ +=(2¹^²x){ 0

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