(b) Compute the flux of the vector field F(x, y, z) = y i– 2.xyk over the triangle T with vertices (1,0, 0), (0, 1,0), and (0, 0, 2).

Q: Compute the upward flux of the vector field Ĥ(x, y, z) = (x, 0, 2z) across the portion of the…

A:

Q: Compute the circulation of the vector field F=(4cos(y))i+(3x^2sin(y))j around C. Where C is the…

A:

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

A:

Q: 4. Find the positively oriented flux over the surface created by the paraboloid z = 16 – x² – y2…

A:

Q: Find the outward flux of the vector field F = (x³, y³, z²) across the surface of the region that is…

A:

Q: Compute the flux of the vector field F(x, y, z) = (2y, 3, –2xz) through the surface S, which is the…

A: Given vector field is, Fx,y,z=2y,3,-2xz. The given surface is, y=x2+z2  and  x2+z2≤1. Now for the…

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

A:

Q: Consider the vector field F(x, y,z)= 2.xy i+(x² +z² ) j+2yzk. c) Is F a conservative vector field?…

A:

Q: Compute the flux, || Foñds, across the slanted face of the tetrahedron 2 = 4-1- y bounded in the…

A:

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: 4. Compute the outward flux of the vector field F(r) = (r, y', =') through the unit sphere r² + y² +…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Compute the net outward flux of the vector field F = (x i + y j + z k)/ (x2 + y2 + z2)^(3/2) across…

A:

Q: Consider again the vector field F = (x +y)i + (x² + y²)j_what is the downward flux across the line…

A:

Q: Compute the flux of the vector field F(x, y, z) = 6ỉ +3j + 2k through the rectangular region with…

A:

Q: b) Find the flux of the vector field F(x,y,z) = 3xi – yj + 2zk; across o where o is the portion of…

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

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

A:

Q: Find the flux of the vector field F(x, y, z) = (yz, y°, xz) %3D across the surface S, where S is the…

A: Given

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, y³), out of the annular region between the x? + y? = 1…

A:

Q: Determine whether the vector field…

A:

Q: (c) Determine the flux of the vector field F = x³i – 2yĵ + 7z²k across a cone z = x2 + y2 + 3 that…

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: Evaluate the outward flux of the vector field F = (2x? – 5e" + sin(2²), –4ry + ln(x*), 5z – 3x²y°)…

A: Given

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: 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: Calculate the flux of the vector field F = -2i + 5æ²j – 3k, through the square of side 2 in the…

A:

Q: Compute the flux of the vector field 1 F(x, y, z) = -k x² + y2 + 1 out of the conical container K =…

A:

Q: Find the flux in the upward z direction of the vector field F(x, y, z) = (xz³, yz³, (x² + y²)²)…

A:

Q: Find the flux of the vector field F = (y, – z, x) across the 2 + 4x + 3y above the rectangle part of…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Given that the vector field F(x, y) = (2x-3y, 2y-3x) is conservative in the xy-plane. If (x, y) is a…

A: We have to find the value

Q: Compute the flux of the vector field F(x,y, z) = yi– 2xyk over the triangle T with vertices (1,0,0),…

A:

Q: Compute the flux of the vector field F(x, y, z) = 3x + 3yk through the surface S, where S is the…

A:

Q: Find the flux of the vector field F = 2 i +3 j – 2 k through the rectangle with corners at (1,0,0),…

A:

Q: Compute the flux

A: Compute the flux

Q: Find g(x, z) so that F(x, y,z) = (8x cos y sin? z + 2e2xz)î – (4x² sin y sin? z)j+ (g(x, z) cos y +…

A: Given that    Fx,y,z=8x cosy sin2z+2e2xz i^-4x2 siny sin2z j^+gx,zcosy+2e2xz k^ Now we have to find…

Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 3+ 4x + 2y above

A:

Q: Compute the flux of the vector field F = zi + 8xk through the parameterized surface S oriented…

A:

Q: Calculate the flux of the vector field F = x²i+ zk across the portion of the plane described as z =…

A: According to our company policy, we are supposed to answer only first question. For the rest please…

Q: Determine if the vector field F(x,y,z)= (yz,xz+2y,xy+1) is conservative. If it is, find its…

A:

Q: Compute the flux of the vector field F = xi + yj + zk through the surface S, which is a closed…

A: Given F=xi+yj+zk ,-3<=x<=3,r=1

Q: Consider again the vector field F = (x + y)i + (x² + y² )j. What is the downward flux across the…

A:

Q: Compute the flux of the vector field F(x,y,z)=5xj+2yk→through the surface S, where S is the part of…

A: Flux problem...

Q: Find the flux of the curl of the vector field F(x, y, z) = [(z2 −4) cos(xyz), 3x+y,(z2 −4) sin(ex…

A: Surface is oriented outwards. And -2 <= z <= 2

Q: Compute the flux of the vector field F(x, y, z) = 41 + 45 + Sk through the rectangular region with…

A:

Q: Find the flux of the vector field F = xi - 3y j - 2z k through the part of the plane 2.x + 3y + z =…

A: The given problem is to find the flux of vector field F through the part of the plane given in the…

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

A: The objective is to find the flux.

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: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…