verify the Its Stoke For Upper Projection theorem Vector Field F = (2x-y)i - yzj- y²zK ² Surface the half on over of x² + y² + z ² bounded xy-plane by

Q: For the vector field F(x,y) =(2xy²+2y)-i+(2x²y+2x)•j a) show that_F_is conservative vector field; b)…

A: Vector field and integration

Q: Parametrize a path for the curve that is a circle in the x-y plane that has radius 2 (a) with center…

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Q: Using Gauss' theorem to calculate the flow of the vector field 3x3 F: F (x, y, z) = (x^2z, 2x^2,…

A: As per the question we are given a vector field F(x, y, z) and we have to use Gauss's Theorem to…

Q: Calculate div F and curl F.

A: F(x,y) = F1i + F2j F1 = x - y2 + 2 F2 = xy + y

Q: 2) If F(x, y, z) = x²i + y²j + 3zk is a vector field, use Divergence theorem to calculate the…

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Q: a) Find the values A and B that allow the vector field given below to be conserved. F(x,y,z)=2xlnz…

A: (a) Given vector field is Fx,y,z=2xlnz i+3Bz j+x2zA+y3k Now, F1=2xlnzF2=3Bz F3=x2zA+y3

Q: Consider the function f(x, y) = (e - 3x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a…

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Q: Find curl(curlF→(x,y,z)) of the vector field F→(x,y,z)=x^9zi→−9x^8zj→+yzk→. Enter the exact answer.…

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Q: Let F = (x^2 + y^2, x^2 + y^2) be a vector field and C be the simple closed curve given by circles…

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Q: Let F-yi + xyj+-xyzk and let Σ be the part of the cone z =sqroot(x^2 +y^2(Figure 3) for 0 < x²+ y²…

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Q: Evaluate the surface integral fof the scalar feld 1-62+4 where S is the surface parametrised by (u,…

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Q: erify Stokes Theorem for the ve lane x + y + z = 1 bounded b orientation.

A: It is given that F→=3x,2x-y,3y is a vector field on plane x+y+z=1 bounded by x=0, y=0 and z=0 with…

Q: 7) Consider a vector field F(x, y, z) = 3yi − xz j + yz².k. Let S be an equation of 2z = x²+y²…

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Q: Find the work done by the vector field F =( y+x 2, 2%y+z, 2yz + 2) %3D the Curve C ( all over it)…

A: The given vector field is F→=y2+xz,2xy+z2,2yz+x22 and a vector field F→ connects points 1,-1,-1 to…

Q: Find a vector valued function which gives the curve of intersection of  y2 + z2 =16  with the plane…

A: Given the curves:

Q: The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In…

A: Solution is uploaded below.

Q: Use Stokes' Theorem to evaluate ( r(t) curl (F) · ds). F(x,y,z) = 2x + 2yj + zk S is the hemisphere…

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Q: 5 Let fi R²→R be the vector field given by F (x,y)- (4,-x). A- Calculate the circulation of f when…

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Q: 1)Let F be the vector 1/yi +1/xj let C be the curve xy=4 from P=(1,4) to Q=(4,1) 2) Evaluate…

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Q: Find a formula F = (F₁(x, y), F₂(x, y)) for the vector field in the plane that has the properties…

A: Answer :

Q: Let Σ be a closed surface with positive/outward orientation. Circle any of the vector fields below…

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Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

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Q: Let C' be the straight line curve between the points (0,7) and (1,0). Let N be the unit normal…

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Q: Given the vector field F = (r + y)7+ (r – y)7, evaluate it's line integral over the plane curve a? +…

A: Line integral

Q: termine if F~ (x, y, z) ), where F~ (x, y, z) = e^x*sin (y)ˆi+e^y*sin (z)ˆj+e^z*sin (x)ˆk. is a…

A: Given,         F→x, y, z=exsin(y)i^+eysin(z)j^+ezsin(x)k^

Q: Verify Gauss's theorem for the vector field = y²i+xz³j+(2-1)³ and it is the enclosure bounded by the…

A: Divergence Theorem:The divergence theorem relates the flux of a vector field over a closed smooth…

Q: Verify Green’s Theorem for the vector field F(x, y) = (x^2*y^2 , xy) and the closed curve C…

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Q: True or False: Let F(x, y) be an incompressible vector field for which div(F) = 0. Let C be the…

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…