Calculate the vector field flux leaving F(x, y, z) = xi + yj + zi solid bounded by the surfaces x² + y² + z² = 10 and z = 2 + x² + y².
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- Find all the integral curves of the vector fields, indicate the domains of each vector field, and obtain two integral surfaces in each case (a) V = (y,-3,0), (b) V = (1, y, ry(22 + 1)). %3D %3DCompute the flux of the vector field = yi + 53 − xzk through the surface S, which is the surface y = x² + z², with x² + z² ≤ 1, oriented in the positive y-direction. flux =Calculate the flux of the vector field F = 6i + 2x²j – 2k, through the square of side 4 in the plane y = 7, centered on the y-axis, with sides parallel to the x and z axes, and oriented in the positive y-direction. flux =
- Calculate the flux of the vector field F(x, y, z) = (4x+8) through a disk of radius 6 centered at the origin in the yz-plane, oriented in the negative x-direction. Flux=Express the vector field B = (x^2- y^2)ay + xzaz in spherical coordinates at ( 4, 30o, 120o) * Express the vector field B = (x2 – y²)ay + xza, in spherical coordinates at ( 4, 30°, 120°) 6.78ar + 0.232ae + 9aØ -3.87ar - 0.332ae + 5aØ -9.87ar + 0.232ae + 6aØ O -3.87ar + 0.232ae + aØFind the flux of the vector field F = (y, -z, x) across the part of the plane z = 3 + 2x + y above the rectangle [0, 3] × [0, 2] with upwards orientation. plz help
- Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and y2+z2=32y2+z2=32 at the point (−4,−4,4)(−4,−4,4).Find the flux of the constant vector field =-i-j+ k through a square plate of area 25 in the xy-plane oriented in the positive z- direction. flux =Compute the flux of the vector field F = xi + yj + zk through the surface S, which is a closed cylinder of radius 4, centered on the y-axis, with -2 < y< 2, and oriented outward. flux =