Find the flux of the vector field F = (y, z, x) across the part of the plane z = 3 + 4x + y above the rectangle [0, 4] x [0, 5] with upwards orientation.

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

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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: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

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Q: Consider the force field F(x, y) = (x, y). a) Sketch the vectors F(1,1), F(-2,1) and F(2,0) directly…

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Q: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

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Q: Compute the flux of the vector field (ï³, — xy³), out of the rectangle with vertices (0,0), (4,0),…

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Q: Find r'(t), r(t), and r'(t) for the given value of to. Then sketch the space curve represented by…

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Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: d) An open surface F is given by F = {(x,y, z) |z = 4 – x² – y² , z > 0} . Compute the flux of V…

A: V(x,y,z) = <2x+3y,2y+3x,-4z>F={ (x,y,z) : z=4-x2-y2 , z≥0}Consider, g(x,y,z) = z+x2+y2-4…

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: Compute the vector assigned to the pointP = (−3, 5) by the vectorfield:(a) F(x, y) = (xy,y − x)(b)…

A: To Determine : (a) F(x, y) = (xy,y − x)(b) F(x, y) = (4, 8)(c) F(x, y) = 3x+y , log2(x + y) Given:…

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

A: Denote the unit sphere by S If the sphere is closed,  then the flux of v(x, y, z) out of S is given…

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: Find the parametrization of two different curves from the point (2,4) to (3,9). Compute the work…

A: Given point (2,4)  and (3,9)now equationof line passing through two point is given by…

Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Compute the flux of the vector field (x², - xy³), out of the rectangle with vertices (0,0), (5,0),…

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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: 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: FTTT 10 5 10- -5- -10- X TTTTI 1C d.

A: We draw the sketch of vector field with the help of direction and length of vectors .

Q: ed by F(x, y) = (-: %3D

A: The function given is , F→x,y=-x,y. Draw the table for the points plot on the graph for the vector…

Q: Compute the flux of the vector field F = yi + 5j - xzk through the surface S, which is the surfac y…

A: A vector field F→=yi^+5j^-xz through a surface S, which is the y=x2+z2  , x2+z2≤1. To Find: The flux…

Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: 2. Consider the vector field F(x, y, z) = 5zi - 7y3j+5xzk. (a) Calculate div F at the point (1,1,0).…

A: The divergence of a vector field is a scalar function that gives the quantity of a vector field's…