Given a vector field F = 5(x² + y²)i+ 2xyj - 3zk, evaluate SSS, V· FdV for which the solid D is formed by a paraboloid x² + y² + z = 10 in the first %3D octant.

Q: Given the vector field E = 4zy² cos 2xa, +2zy sin 2xay + y² sin 2xa₂ for the region [x], [y], and…

A: The general form of a vector-valued function in three dimensions is given by F=F1ax+F2ay+F3az, where…

Q: What is the (numerical) value of the 3-form field (x² + y + z?) dx A dy A dz on the ordered triple…

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Q: Is the vector field F(x, y) = 2xy+y 2xy+ xy+y*x x conservative? Select the correct answer below: O…

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Q: Find the divergence of the vector field F = ā x7, if r = xi+yj+ zk and ā = 3 i+3j+9k, by first…

A: First of all we calculated the vector F by calculating the vector product of the vectors a and r.

Q: 4. Consider the vector field given in Cartesian coordinates by A(r) = (x² + y³, 3xy², z²). (a)…

A: Given : Ar=x2+y2,3xy2,z2

Q: Compute the flux of the vector field F = xi + 5yj through the cylindrical surface as shown in the…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj + +x ' ||||||||||| 畫 至 X

A: Solution is given below:

Q: Given a two-dimensional vector field F and a smooth orientedcurve C, what is the meaning of the flux…

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Q: Consider the vector field F = (5x + 6y, 6x + 4y). F - dr along the curve C given by r (t) = (t², t*)…

A: ∫CF→·dr→=∫abF(r(t)) r'(t) dr

Q: Find the flux out of the unit shpere for the vector field F(2,4, ;) = 1ā+3+K). %3D r answer =

A: Flux of F through the closed surface S is ∫∫sF→·n→dsS is the unit sphere x2+y2+z2=1Letϕ:…

Q: For the vector field F(x, y, z) = (15x2y + 2xz)i + (5x3 + 35y4)j + x2k, show that F is conservative…

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Q: Evaluate both sides of the divergence theorem for the vector field D = 2xyx + x²9 [C/m²] and a…

A: This question is belong to the vector calculus in which we have to deal with the divergence theorem…

Q: Evaluate , (V. A) dV for the vector field A = x²yi +xz³j- y²z²kwithin the volume of a cube defined…

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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: Is the vector field F = y? – 2x², 2xy + 3| conserva Yes No yz Is the vector field F y? – x2 con Vy?…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: (b) Given a vector field F = 5(x² + y²)i+ 2xyj – 3zk, evaluate JI, V· FdV for which the solid D is…

A: Here we use polar form of circle .

Q: Consider the scalar field f(x,y, z) = 2x² – y² + 3z? Determine V Vfl(1.-1.1) II. VxVfl1.-1.1)

A: Here, the given function is: f(x,y,z)=2x2-y2+3z2

Q: for the vector field F = 2xz i+ (1 – 4xy² ) j led by the plane z = 6 – 2x² – 2y² and the plane

A: We have to find the following conditions according to the given information

Q: Given a vector field F = (x + xy?)i + (5xy)j. Use Green's Theorem to evaluate F- di where C is a…

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Q: Show that the vector field F = x²i + (2yz)j+ y² k is conservative and then find the corresponding…

A: A vector field F is conservative if curl(F)=0 or ∇×F=0 The potential function is given by f such…

Q: Compute w(v), where w =(x-y)dx+(x+y)dy is a covector field and v = (x/y)d/dx-(y/x)d/dy is a vector…

A: Given: w =(x-y)dx+(x+y)dy  v = (x/y)d/dx-(y/x)d/dy

Q: Match the vector field with its graph. F(x, y) = xi + 3yj -st

A: Plot the given vector Fx,y=xi+3yj.

Q: Is the vector field F (x, y) = (2xy – y³) î + (x² – 3xy²) ĵ solenoidal, conservative, both or…

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Q: given the vector field A(r,θ,φ )= sin(θ)*r + r*θ + 6*φ, find the laplacian and evaluate it at the…

A: In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence…

Q: Find the flux of the vector field F = through the half-sphere z = V1 - x² - y2. none of these above…

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Q: Consider the vector field F = (r²y³, x°y?) Is this vector field conservative? Conservative If so:…

A: Given the vector field <x2y3,x3y2>. We need to: i) Check whether the vector field is…

Q: How much work is required to move an object in the vector field F = 5 y² ỉ + 2xy] Along the curve C,…

A: Given: F=5y2i+2xyj  C1 is the line y=0 C2 is the line x=1 C3 is the line segment joining points 1,1…

Q: Given the vector field F (x, y, z) = 2xyi + (x² + z?) j +2yzk a. Verify that the vector field…

A: Ans :A)

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5

A: We can solve this using by draw a graph

Q: Find a potential function for the vector field F by inspection. (If an answer does not exist, enter…

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Q: Show that the vector field F = 2.xyi + (x – 2 y)j is conservative and evaluate the line integral %3D…

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Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

A:

Q: Find the work done by the vector field F = (- 3z, 4y, 2x) in moving an object along C in the…

A: Work done by any vector field F is given by ∫F.dr where r is the position vector. Dot product is the…

Q: (10) Given that the vector field F= 2z i- 3 x j + 4 y k Evaluate f F. dr where S is the portion of…

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Q: Compute the curl of the vector field F = -2z i – 3y j – 5x k.

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: What is the value of a so that the vector field F(x.y)=(y eX+2xy4) i+(ax2y3+ e%) j is conservative?…

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Q: Show that the vector field F = 2.xyi +(x² – 2 y)j is conservative and evaluate the line integral…

A: Given the vector field

Q: What is the value of a so that the vector field F(x.y)-(y eX+2xy4) i+(ax²y3+ e%)j is conservative? O…

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Q: Given the vector field F(x, y, z) = (2z3 – 4y2 + axy,x² - 8xy – bz, 6xz? –- ay + 4), compute the…

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Q: Show that the vector field F(x, Y, z) = (x² + y²)i – 2xyj is not conservative on R³.

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Q: What is the value of a so that the vector field F(xy)=(In y+2xy³) i+(ax3y2+ x/y) j is conservative?…

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Q: Find the divergence of the vector field V(x, y, z) = -2e*'i – e³xyj+ 7e%yzk.

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Q: Determine whether F(x, y) = (In(y) + 2xy³) i+ (3x?y? + x/y) j is a conservative vector %3D field. If…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj KE 、 ||十

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Q: Use Gauss's Theorem to evaluate fF.ds for the vector field, F = x³ į+ y³ į+z³k, taking S S to be a…

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Q: Given the vector field F(x,y) = [x/((x^+y^2)^(3/2)), y/((x^+y^2)^(3/2))], Find a fucntion f(x,y)…

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: Given vector field F(x, y) = (4x³y? – 2xy³,2x*y – 3x?y² +6y³) and curve C defined by C: 7(t) = (t+…

A: Here we will find out the required value.