Find the flux of the vector field F = 2 i +3 j – 2 k through the rectangle with corners at (1,0,0), (1,0, 2), (1,3, 2), (1, 3, 0) oriented in the positive direction of x-axis.

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

A:

Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

A:

Q: Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the…

A: v→=y2i→+1.3x2j→ Initial point 1,2 ∆t=0.1

Q: 1) Find the work done by the vector field F(x, y, z) = (x², 4xy³, xy²) on a particle that %3D…

A: Given force is F→x,y,z=x2,4xy3,xy2 Let r→=rt→ be the boundary of the rectangle with vertices  0,0,0,…

Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: Consider the vector field v(x)

A: Given, the vector field        v(x)=yx2+y2i^-xx2+y2j^+6k^                               ...(1)

Q: Find the flux of the constant vector field =-i-2j+2k through a square plate of area 9 in the…

A:

Q: 2.x²y"+xy'–3y= 0,x>0

A:

Q: Compute the flux of the vector field (ï³, — xy³), out of the rectangle with vertices (0,0), (4,0),…

A:

Q: a) Calculate the flux of the vector field F(x, y, z) = 275k through a sphere of radlus 4 centered at…

A:

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

A:

Q: Compute the flux of the vector field F =2xi +3yj through the cylindrical surface shown below, if a=3…

A: Given that the vector field is F(x,y)=2xi+3yj Let us parametrize the cylinder as x=cosθ, y=sinθ, z=r…

Q: d) An open surface F is given by F = {(x,y, z) |z = 4 – x² – y² , z > 0} . Compute the flux of V…

A: V(x,y,z) = <2x+3y,2y+3x,-4z>F={ (x,y,z) : z=4-x2-y2 , z≥0}Consider, g(x,y,z) = z+x2+y2-4…

Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

A:

Q: Find the gradient vector field of f(r,y, z) = x*y* +y³z³ + æz°.

A: The gradient vector field of f(x,y,z) is given by ∇f=∂∂xf(x,y,z) i^+∂∂yf(x,y,z) j^+∂∂zf(x,y,z) k^…

Q: (a) Calculate the flux of the vector field F(x, y, z) = 27 - 4k through a sphere of radius 3…

A:

Q: Consider the vector field F = (2, -3). Let C be the straight line segment oriented from point (3,0)…

A: Given vector field, So,

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

A:

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: Find the flow of the vector field a = (x + 2y)i + (x + 2z)j − zk along the outer surface of the…

A: Given To find the flow of the vector field a→ = (x+2y)i→+ (x + 2z)j→ - zk→along the outer surface of…

Q: Compute the flux of the vector field (x², - xy³), out of the rectangle with vertices (0,0), (5,0),…

A:

Q: ) Show that the vector field, F3 yz £ + zx ŷ + xy 2 c

A: Given: The vector field is, F3 = yz x^ + zx y^ + xy z^