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

Q: 2. Sketch at least ten arrows in the vector field: F(x,y)=(-2y)i + (x+1)j

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Q: F(x,y) = x²yi + 3y³x²j Find the integral curves for the vector field Оа. -бу + 1 = C 6ху? b. -6ху —…

A: given vector field Fx,y=x2y i^+3y3x2 j^ claim- find the integral curves for the vector field

Q: F(x, y, z) = -k At (-2,-2, -2) the vector is At (-2,-2, 2) the vector is At (-2, 2, -2) the vector…

A: Given vector field F(x,y,z)=-k Here k is constant

Q: Express the vector field B = (x^2- y^2)ay + xzaz in spherical coordinates at ( 4, 30o, 120o) *…

A: Relation between cartesian and spherical co ordinate system x= r sinθ cosϕ   , y = r sinθ sinϕ   ,…

Q: Find the directional derative of f at the point P0(1,1) in the direction of the vector A = 3i - 2j…

A: Direction derivatives at (1,1) is given in direction of A = 3i - 2j.

Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

Q: Sketch the vector field. У x F(x, y) = ( - 1/2, 2/2 ) x У 20 0 2 -20 0 -2 2 2 -2 2 -2 -2 2 -2 4 3 3…

A: Step 1:

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 and describe the vector field F (x, y) = (-y,2x)

A: The given vector field is F→x,y=-y,2x A vector field F→ in ℝ2 or ℝ3 is an assignment of a…

Q: 2. For the vector field F(x, y, z) = (x²y, xyz, −x²y²) F(x, y, z)=(x2y,xyz,-x2 y 2 ), find: (a) div…

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Q: 9. Sketch the vector field F(x, y) : :(yi — х). Vx? + y?

A: Consider the given filed, Fx,y=1x2+y2yi−xj Further simplify. Fx,y=yx2+y2i-xx2+y2i=〈yx2+y2,-xx2+y2〉

Q: (c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given…

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Q: Evaluate the 1-form φ = x2yz dx − z dy on the vector field V (x, y, z) = xU1(x, y, z) − yzU2(x, y,…

A: We need to evaluate the 1-form of  ϕ=x2yz dx - z dy.....(1) in the vector field  V(x,y,z) = x…

Q: Calculate the curl of the vector g = (x−y) ax+(y+x) ay, and visualize it. Explain what does "curl of…

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Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

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Q: Which of these vector fields are irrotational? Identify all of those that satisfy this property. A B…

A: The given vector fields, A) u=-x, y, 0B) u=-y, x, 0C) u=-x, z, 0D) u=x, y, z We have to find the…

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

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

A: The solution as follows :-

Q: Calculate vector field F = (2-z²+2-x²)i + (2 · y³ + 4·x)j + (2x²z³+2)k a flux from a box with the…

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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…

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Q: Find the curl of the vector field F(x,y,z)=x^2yi-2y^3zj-3zk.   A. curl F = 2y3i + x2k          B.…

A: Option (c) correct  For detail...go through the solution

Q: The gradient vector field of f(x,y)=y(2x2 -y3 ) is given by: O1. (2xy)i +(x2 -3y² »i O II. (4xy)i…

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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: Let C be the straight line segment in the xy-plane from the point (1, 2) to the point (5, 3). Let F…

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Q: Recognize a vector field in a plane Sketch the vector field. x | y || F(x, y) = (1/2, − 4 ) 2 2 02…

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Q: Find the Curl of the vector field. F(x,y, 2) = 3e" sin(y)i+ 7e* cos(y)j+ &z k cos (y)i+ &z k. %3D…

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Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: Please answer and write correctly and neatly. Given the vector field Ā= 2x2y ax – 2(z-x) ay + 3xyz…

A: Given That : Vector field  A→=2x2yax-2(z-x)ay +3xyzaz Point P=(2,-3,4)  To Find : d) y coordinate of…

Q: Find the curl of the vector field F =< yx5, xz², zyб curl F = i + 1:0 12

A: