2. Don't generate a vector field- answer based on thinking about x and y values (pos, neg, zero....) Describe the vector field for F= a) For when will the vector field be undefined? ( in other words, for what values of x, y and/or z) √√x²+y²+z² b) What can be said about the direction of the vector field when x>0, y> 0, z < 0 x < 0, y < 0, z < 0 x < 0, y> 0, z>0

Q: 4.) Verify the Expansion of the triple vector product A x (B x ) = B⋅ (A·C) - C (A. B) by direct…

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Q: In words, what is a vector field? Give some physical examples of vector fields

A: Vector feild can be defined in 2 dimensions as well as 3 dimensions.A vector field F→ in ℝ2 is an…

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: 9) Check whether the vector field F = (-cos x cos y, sin x sin y, - sec² z) is a gradient vector…

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Q: Sketch the vector field in the plane along with its horizontal and vertical components at a…

A: We shall use MATLAB to plot the given vector field on the circle.  MATLAB CODE F = @(x,y)…

Q: ector product of two vector fields: V × (F x G) = (V · G)F – (V · F)G + (G · V)F – (F · V)G %3D

A: Part iii Given, The identity of the vector product of two vector fields is proved.

Q: 1. If f is a differentiable scalar function and F is a differentiable vector field, which of the…

A: Introduction: In vector calculus, there are many different operations that are performed on scalar…

Q: 5. Using Stokes' theorem, find I (VxF) ndo, where F yi+xj+(y+z) k and S is the portion of the…

A: We have to find I=∫∫S∇×F·ndσ using Stokes' theorem.

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: Find the curl of the vector field F = curl F= [2zy-5xz4] 0 26 Calculator Check Answer X < i + Oj+ x…

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Q: 12. (a) Consider again the vector field in Exercise 8 and its curl. Sketch the vector field and use…

A: a)  F = xi + yj + zk Hence, curl of F becomes∇×F = ijk∂∂x∂∂y∂∂zxyz = i∂z∂y-∂y∂z - j∂z∂x-∂x∂z +…

Q: Sketch several representative vectors in the vector field given by F(x,y)-3yi-xj. b. a. 3 34

A: F(x,y)=3y i - x j F(0,1)=3(1) i - (0) j=3iF(1,0)=3(0) i - (1) j=-jF(-1,0)=3(0) i - (-1)…

Q: onsider the vectors A and B presented below. ind: TA = TB = +BT = BT = A = 26 2 -10 = (345) the…

A: Given A = 26-10  ,  B = 345

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

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Q: When is a vector field irrotational?

A: We have to determine when is a vector field is irrotational.

Q: Find the curl of the vector field F = curl F = i+ j+ k

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Q: 2. True/False: If F, G are vector fields and V × F = V × G, then F = G. (Justify your answer by…

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Q: Give three equivalent properties of conservative vector fields.

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Q: Define the terms sink and source in vector fields.

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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: I the curl of the vector field F = ■ F = j+ k

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Q: But for any vector A and scalar V, the identity or V VA = A.VV + V(V-A) (VA) V = VVA - A VV

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Q: 4. True/False: curl(divF)) is not a meaningful expression. (Justify your answer.)

A: Relation between Crul and div of vector quantities

Q: What are the outputs of a vector field in ℝ3?

A: What are the outputs of a vector field in ℝ3.

Q: 5. Prove that if F, G are vector fields on R3, then curl(F + G) = curl(F) + curl(G).

A: Let the vector fields F and G are: F=Fxi+Fyj+FykG=Gxi+Gyj+Gzk Then,…

Q: Consider the square C oriented counter clockwise, with vertices (0, 0), (2, 0), (0, 2), (2, 2) and 7…

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Q: 2. A vector field is specified as G = 24xy ā, + 12(x² + 2)ā, + 18z²ā,. Given two points, P(1, 2, -1)…

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Q: V(E × F) = F(V × E) – E(V × F). %3D

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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: I dont know how to answer this question, it would be very helpful, if you could ans this question…

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Q: (a) State True or False and proved justification for: If S is an ellipsoid and F is a constant…

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Q: A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of…

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Q: let c is a differentiable vector field then div(curl)=

A: This question is related to vectors.

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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