(a) Calculate the flux of the vector field F(x, y, z) = 3i – 9k through a sphere of radius 2 centered at the origin, oriented outward. Flux = (b) Calculate the flux of the vector field F(x, y, z) = i − 2j + 6k through a cube of side lengt - 2 with sides parallel to the axes, oriented outward. Flux =

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

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Q: Vz(x, y) V + y have the Show that all the vectors in vector field F same length, and state the…

A: The length or magnitude of a vector a, b is defined as follows: a, b=a2+b2 Note ca, b=ca, b, where c…

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: 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: 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: The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end…

A: Given, vector field F→x,y=2xy,x2 and three curves that start at 1,2 and end at 3,2.

Q: Find the flux of the vector field V(x, y, z) = 9xy²i + 9x²yj + z³k out of the unit sphere.

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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: a) Calculate the flux of the vector field F(x, y, z) = 275k through a sphere of radlus 4 centered at…

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Q: Find the flux of the vector field F = across the part of the plane z = 3 + 2x + 4y above the…

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Q: Compute the flux of the vector field F =2xi +3yj through the cylindrical surface shown below, if a=3…

A: Given that the vector field is F(x,y)=2xi+3yj Let us parametrize the cylinder as x=cosθ, y=sinθ, z=r…

Q: Calculate the flux of the vector field F(x, y, z) = (4x+8) through a disk of radius 6 centered at…

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Q: Q1: a) Sketch the vector field and find the fixed points of the following function i = x - V1 -…

A: Given equation is x.=x-1-sin2x and we have to find the fixed points of this equation. We will use…

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 flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

A: A constant vector field  and a square plate of area 25 in the xy plane oriented in the positive z…

Q: Find the flux of the vector field V(x, y, z) = 2xy²i+ 5x²yj + 3z³k out of the unit sphere. Flux =

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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 F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

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Q: = + 1³ 2³ +²²³ +22+ Calculate the flux of the given vector field F where S is the sphere centered at…

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Q: Sketch the vector field: F(x, y) = (1, 2y) Carefully draw at least four vectors in each of the four…

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Q: Calculate Vø and V?o of the scalar field: 6 = eV=²+y?+z?

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Q: PART A ] (1) Find a complex potential function g(z) of the given vector field F (x,y). (2) find the…

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Q: Sketch the vector field of F = (-y,0) in the xy-plane. %3D

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