Part 1 Part 2 A vector field gives a geographical description of the flow of money in a society. In the neighborhood of a political convention, the divergence of this vector field is: negative positive zero Evaluate the integral (sin x + 2y)da + (7x + y)dy for the nonclosed path ABCD in the figure. A= (0,0), B- (2,2), C-(2,4), D- (0,6) parallelogram

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: Find the curl of the vector field F = (7x sin(y), 3y cos(x)). curl F

A: The given vector field F=7xsiny, 3ycosx. The objective is to find the curl F. Use the derivative…

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

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Q: Find the flux of the constant vector field =-i-2j+2k through a square plate of area 9 in the…

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Q: Match the vector field with its graph. F(x, y) = yi 5 5 -5+ サ

A: To match the given vector field to its graph, where given graphs are given below.

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: (a) Calculate the flux of the vector field F(x, y, z) = 27 - 4k through a sphere of radius 3…

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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: Assume that an object is moving along a parametric curve and the three vector function T (t), N(t) ,…

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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: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

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Q: Using arrows, clearly sketch the vector field u(r) = (y², x + y, 0) in the (x, y)-plane.

A: Given the vector field function u(r)=(y2,x+y,0). We need to plot the vector field in the…