Find the flux of the vector field F = xi - 3y j - 2z k through the part of the plane 2.x + 3y + z = 6 in the first octant, oriented upward. 1.

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

A:

Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 3x2j -z2 k;…

A: F = 3x2 j -z2 k,y = 2x2,0≤z≤2,-1≤x≤1.

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: Find a flux of the vector field ä(M)= (2z– y)i +6xj + yk through a part of the surface S: x - 4y+2z…

A: Given, a→M=2z-yi^ +6x j^ +y k^ Also given surface is, S: x-4y+2z-4=0 So the normal vector to the…

Q: Calculate the flux of the vector field F(x, y, z) = 5i + 2j+ zk through the closed circular cylinder…

A:

Q: Find the flux of the vector field F k through the upper half of the sphere x + y + z² = 4. %3D pi…

A:

Q: Find the outward flux of the field F = (x + y)î + yĵ + zk across the closed surface: S: z = 16x² -…

A:

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: Consider the gradient vector field V = Vg of the function g(x, y) = x² + y² + e*²-y´ cos(2xy).…

A: We will use the Divergence Theorem in 2D to solve the given flux integral.

Q: Find the flux of the field F = y2i + xzj - k outward (normal away from the z-axis) through the cone…

A: Definition:

Q: Find the flux of the vector field V(x, y, z) = 6xy²i + 7x<yj + z°k out of the unit sphere.

A:

Q: Find the flux of the vector field F across the surface S in the indicated direction. F=x2y 5i+yj - z…

A: we have to find the flux of the vector field F=x2y5i+yj-zk across the surface S: portion of the…

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

A:

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

A:

Q: 2.) Calculate the curve integral over the vector field V(17, y) = ( * -2²y xy? for the positive…

A: Disclaimer: Since you have asked for a handwritten solution and currently we are not providing any…

Q: Find the flux of the vector field F = 2r2i+ 2y²j+ 4k across o in the direction of positive…

A:

Q: Compute the flux of the vector field F = 2xi + 5yj through the cylindrical surface shown below, if a…

A:

Q: Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of…

A:

Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = Jx2 + y2 + 3 that…

A:

Q: Calculate the flux of the vector field (x°, y), out of the annular region between the a + y? = 16…

A:

Q: 4. Consider the vector field F = (y?2³ + y)i+ (2æyz³ + x – 2)j+ (3xy²z² – y + 3)E. (a) Verify the…

A:

Q: Calculate the flux of the vector field (x, y³), out of the annular region between the x? + y? = 1…

A:

Q: Calculate the work done by the vector field F(x, y)= ,2xy) on a particle that moves once around the…

A:

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: Q1 Use Stokes theorem to compute the flux of the curl of a vector field F = (2x – y)ĩ – yz? j- y²zk…

A:

Q: Calculate the flux of the vector field through the given surface.  F = 2i −3j + 6x2yk through the…

A:

Q: Find the flux of the vector field F across the surface S in the indicated direction. F =x3y 2i+yj…

A:

Q: Show that the vector field given below is conservative and find its potential function. F(x, y) =…

A:

Q: Compute the flux ∫F · n ds of F across the curve C for the given vector field and curve using the…

A: Solution; Consider the given function: F(x, y) = xy, x-y = P, Q P = x y Q = x -y and the boundaries…

Q: Q.3) Use the divergence theorem to find the outward flux of the vector field F(r, y, r) = ri %3!…

A: Here, Fx,y,x=xi

Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

A:

Q: The vector field F = (, i, 2²) has a scalar potential in the region R= {(x, y, 2) E R³ : r² + y? >…

A: We find out true or false.

Q: 2. Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across o, where o is the portion of…

A: The given problem is to find the flux of the given vector field over the given portion of cone…

Q: Find the flux of the field F = 4x i + 4y j + 2 k outward (normal away from the z-axis) through the…

A:

Q: (b) Solve the electric flux through a paraboloid z = x? +y² – 16 that lies below plane %3D z= 0. It…

A:

Q: A conservative vector field is given as F = 6xe'i + (3x²e" –10yz')j-15y²z°k. Find the potential…

A:

Q: Compute the work done by the force field F = , 0 <t<1

A:

Q: Show that the vector field F = i + sin(z) j + y cos(z) k is conservative and then find the…

A:

Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 8x i + 8y…

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: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Determine whether the vector field is conservative, and, if so, find a potential function. (If the…

A: If curl of vector field is zero then conservative otherwise not conservative

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…

A:

Q: 16. Compute the flux V· nds of the vector field V(r, y) = (x² – 2ry, y² – 2xy) across the curve C :…

A: We have to compute the flux ∫ℂV·nds of the vector field Vx,y=x2-2xy,y2-2xy across the curve…

Q: Determine whether F(x, y) = e5 cos 5y i – e5" sin 5yj is a conservative vector field. If so, find a…

A: ANSWER :

Q: Find the flux of the field F = z k across the portion of the sphere x2 + y2 + z2 = a2 in the first…

A:

Q: A. Find the flux of a vector field = 8x i + 6y j+ 2z k through the portion of the plane z = 7 where…

A: As per the guidelines, I am supposed to do the first question only. Kindly repost the second…

Q: Find the outward flux of the given field across the given cardioid. F=(3ry-)i+(e*+5tan-'y)j 1+y?…

A: The outward flux of given field is given by using greens theorem.

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…