Consider the vector field F (x, y, z) = (y - zsinx, x, 2z + cosx). The work that performs the F field to displace a body, from point A (3π, −1, 1) to point B (π, 2, 0) corresponds approximately to:

Q: Find an equation of the plane through the origin such that the circulation of the field F = zi + xj…

A: Given the circulation of the field F = zi + xj + yk along the intersection of the planeand the…

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

A:

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: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = −1xyi – 2yzj —…

A:

Q: The vector field F = ( , ,2²) has a scalar potential in the region R= {(r, y, z) E R³ : x> 0}

A: ANSWER: TRUE

Q: If a vector field F (x, y, z) = (evz-, In (x² z), sin z), which of the following values is equal to…

A: We have to find div F(-1,0,1).

Q: Let F = (0, x), a 2D vector field. Compute fF . T ds, where C is the top half of the circle of…

A:

Q: . Consider the vector field F(r, y, 2) = (8r sin y, 4x² cos y – e"z, -e" – sec² z). %3D | F. dR…

A: For a vector field F→, the line integral about the path C is ∫CF→·dr. Let rt be the parametric…

Q: Find the curl of the vector field F(x, y, z)= e sin yi - e cos yj.

A:

Q: Consider the vector field F(x, y, z) = (2xy, x², 1). (a) By calculating the curl of F, show that F…

A:

Q: Consider the vector field F(x, y) = yî- xî+ zR and path joining (1, 0, 1) and (-1, 0, 1) as C;:…

A:

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

A:

Q: (b) Verify Green's Theorem for a vector field F(r, y) = cy'i – ya'j on a disc with center (0, 0) and…

A:

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

A:

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

A:

Q: Consider the vector field F (7x + 5y, 5x + 4y). O The vector field is not conservative O The vector…

A:

Q: Compute the curl of the vector field F = sin(x) i+ cos(y) j+ 8z3 k

A:

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

A: Solution :

Q: Show that the vector field F (x, y, z) = xz i + xyz j y 2 k is not conservative.

A: Consider the following vector: Fx,y,z=xzi^+xyzj^+y2k^ Find the Curl of F→:…

Q: Find the curl and divergence of the vector field. F(x,y,z)=x^2yz i -x x^3y k

A:

Q: Consider the vector field F = 5 sin(x² )ï + (3x² + 2e* )j. Find the line integral F· dr, where C is…

A:

Q: Let W be the work done by the forced field F(x,y,z) =yi+zj in order to move a particle along the…

A: The formula for work done is W=∫F.dr.

Q: Find the flux of the vector field F(x, y, 2) = yj + k where o is the portion of the cone =' = 4(x² +…

A:

Q: Determine whether the vector field…

A:

Q: Given the vector field F(x,y,z) = [x, y, -2z] satisfies div(F) = 0. Find a vector field G(x,y,z)…

A:

Q: find the work done by the given vector field F along the specified curve C.   F(x, y) = yi − x j,…

A: Given, F(x,y)=yi^-xj^ where curve, x2+y2=4 W=∫F.dr W=∫ydx-xdy from curve, dx=-dy W=∫xdx+ydy limit of…

Q: Зу 1. Given the vector field F(x, y, z) = î+ Vrz j+x cos y - k, find curl F and div F.

A:

Q: Consider the vector field F = 2xy i + (x2 + 2y) j. Verify the Green's Theorem in the closed region…

A:

Q: Consider the vector field F = (a*y°, æ°y*) Is this vector field conservative? Select an answer If…

A:

Q: Compute the work done by the vector field F(x, y) = (ry, x² + y³) when moving a particle…

A:

Q: The divergence of the vector field F(z, y, z) = (ya°, az", zy?) is: %3D

A:

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

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: Consider the vector field F(x, y) = (x², −y). If (x, y) is in the first quadrant then the vector…

A: Part 1. (x, y) is in the first quadrant.  => x > 0 and y > 0 => x2 > 0 and - y < 0…

Q: Consider the surface integral of the vector field F= [xy², 3x², x²z]over a surface S, where S…

A: From Gauss divergence theorem, we have ∬SF→⋅dS=∭VdivF→dV   The vector field is F→=xy2,3x2,x2z.…

Q: Consider the vector field F = (x*y, x*y? Is this vector field conservative? Select an answer If so:…

A:

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: Consider the vector field F(z, y. 2) = -3yzi +(-3rz +2yz²)j+ (-3zy+ 2y°z + 1)k. (a) Calculate curl F…

A: Note: As in the part (B) the page 94 is missing, so we are solving one (a) part of the given…

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

A:

Q: Consider the vector field F(x,y,z)=(−3x^2,8(x+y)^2,9(x+y+z)^2). Find the divergence and curl of FF.…

A:

Q: F(x, y, 2) = (y² cos r + 2*)i+ (2y sin æ – 4)j+ (3xz² + 2)k Cos z

A:

Q: The vector field F(r, y) = (2xy +y) dx + (æ + 2xy) dy is conservative. %3D The function f(x, y) = x²…

A:

Q: Find a field F = M(x, y)i + N(x, y)j in the xy-plane with the property that at each point (x, y) ≠…

A:

Q: Consider the conservative vector field given by: F (x, y) = (x - ycos (x), y - sin (x)) A potential…

A:

Q: Determine the flux of the vector field F = x³i – 2yĵ + 7z?k across a cone z = /x2 + y2 + 3 that lies…

A: Gauss theorem states that if V is a volume inclosed by a closed surface S then  flux=∫∫S F.n dS=∬∫V…

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)…

A:

Q: Determine whether the vector field…

A:

Q: B) Find the work done by the conservative vector field F (x, y, z) = yzi+xzj+xyk along a smooth…

A: Since, it is given that the field is conservative.

Q: Let C be the helix that winds around the cylinder x2+y? = 1 (counterclockwise viewed from the…

A: here i used parametric equation of helix and done simple calculation like dot product and after that…

Q: Evaluate F Î ds for the vector field F(x, y) = yì – xj counterclockwise along the circle x² + y² = 1…

A: