Given a vector field is conservative. find a potential function 9 for F(x,y,z) = óxi + 4yj+ 1ázk a. d = 3x2 + 2y-&2+ C Ob. Ø = 3x² + 2y² + &z? + c ²+2y²+&z + C $ - 3x - 2y? + 82? + C d. 3 2. 2 2 8. z* + C No correct answer

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   ,…

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Q: 1. Find the curl of the following vector fields: (a) F = cos(e)i + √y³ +y6 + y²j+z¹+tan² z k. (b)…

A: As per Q&A guidelines we solve only part (b) and you can reposted next question seperately.

Q: Please draw a graph that is a proper subgraph of the following graph (by "proper subgraph", I mean…

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Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then

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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: Find the curl of the vector fleld F(z, y) = 9ye" i+2ejat the point (-2, 0). Enter an exact answer.…

A: F(x, y)=9y2 ex3 i +2x2 ey jcurl F→=∇×F→curl F→=ijk∂∂x∂∂y∂∂z9y2 ex32x2 ey0         =∂∂x(2x2…

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

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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: Describe the vector field by drawing some of its vectors. F(x, y) = 5xi - 5yj WebAssign Plot

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Q: If A =  (2   1) and  B = (3 )then BA =            (3   4)                (1)

A: Given A=2134 and B=31

Q: -(4,2) use it to evaluate F. dr (1,0)

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Q: sider the vector-valued function R(t) with Ả(1) = (1,2,−1) and Ř'(t) = = 1 2 (²²/7/7 - 2) - Find…

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Q: Suppose the vector field v(x, y, z) = (4xy2, -4xz², 5x) represents the velocity field of a fluid.…

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Q: (c) Calculate the divergence (V.Ä = div Ã) and curl (V × Ā = rot Á). of the following vector fields.…

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Q: If the following vector function are equal to: A(t) = 5*t i + 2*t^2 j B(t) = 3*t^2 + 2 j Then…

A: The given problem is to find the derivative of the dot product of the two vector functions. Given…

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: x = sup(A) and if a ɛ A, with x#a , then which of the following statements is Let true? O There is…

A: Given that x is sup(A) . We have to check which of the following statement is true or false.

Q: Sketch a sample of vectors for the vector field F(x, y) = (4x,4y) Choose the correct answer below. O…

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Q: Given two vector fields E = 5xya, + 6(x + 3)a, + 8z'a, D = yza, + xza, + xya, (a) Evaluate C= D+E at…

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Q: Let be a vector field and fbe a scalar point function, then curl (f) is equivalent to (1) 2. (grad…

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Q: Q1. Find the vector function r(t) given that r(0)= i+2j. and r'(t)= (2et, 3t², 4 cost)

A: The given data is: r0=i+2jr't=2et, 3t2, 4cost Find the vector function rt