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: Consider the vector field: F = (ex, In(xy), e xyz) (i) Find div(F) (ii) Find curl(F) (iii) Find…

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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: 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: Compute the curl of the vector field F = (x³, y³, 24). curl(F(x, y, z)) = What is the curl at the…

A: F→=x3, y3, z4

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: QI-A) Fnd the position, vekocity and the speed of the vector function ( r(t) ) that given bekow at…

A: Given vector function is r(t)→=t2i-t3j To find the position, velocity and the speed of the vector…

Q: Find the gradient of the function f = xyz-4y z.

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Q: Find the angle between the surfaces x² + y² + z² = 49 and z = x² + y² - 7 at the point (3,-2, 6):

A: Since you posted multiple questions, as per Bartleby guidelines we are answering here first…

Q: Let ß be the vector-valued function 3u B(u, v) = { 32 ß: (-2, 2) × (0, 2π) → R³, 3u² + 4 COS(V) } u…

A: Since you have asked multiple questions, we will answer the questions (a) and (b) for you. If you…

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: vector field F = ⟨b cos(ab) + 2a + b, a cos(ab) + 2b + a⟩. State if it is conservative with reasons.

A: The given vector field If the vector field  is conservative Then

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

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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 vector field is specified as G = 24xyax + 12(x² + 2)ay + 18z²az. Given two points, P(1, 2, - 1)…

A: Given: G=24xyax+12x2+2ay+18z2az P1,2,-1 Q-2,1,3 To find: c Unit vector directed from Q to P. d…

Q: Consider the vector field F = |y² + xz, x² + yz, z² + xy| Find each of the following values (or…

A: The answer is given as follows

Q: 1-2 Find the domain of the vector function. 1. r(t) = (10(1 In(t + 1), t - 2:21

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Q: Sketch the vector field. 8 2 0 -2 0 y 0 2 0 -2 F(x, y) = (2, 2) = 2'

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Q: Match the vector fields with the appropriate pictures. (a)(ア) (b)(ア)=ア (c)(x)=x (d) F(x,y)=x (0)…

A: We have to match the vector field with the appropriate diagram

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: Sketch representative vectors for the vector field by sketching it's scalar field. F(x, y) =…

A: Given: Vector field ,Fx,y=-12yi^+15xj^We need to sketch the scalar field using representative…

Q: Given the vector field F = (8xz+y², 2xy, 4x2). Find its curl. Assume the curl vector is (a,b,c),…

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Q: - Format: Find the directional derivative of f(x, y, z) = -4x²z - 11 xy + 2z² at P = (-3, -3, -2) in…

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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 longest interval in which the following initial value problem is guaranteed to have a…

A: Consider the initial value problem    y"+P(x)y'+Q(x)y=g(x)y''(x0)=a                 y'(x0)=b If…

Q: Find the vector field the graph describes. X

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