Let S be the part of the plane 2x + 3y+ z = 3 which lies in the first octant, oriented upward. Find the flux of the vector field F = 1i+2j+3k across the surface S. 0

Calculate the flux of the given vector field across the surface S..

Find the flux of the vector field F = xi + ex j + zk through the surface S given by that portion of the plane 9x+y+7z = 4 in the first octant, oriented upward.

Sketch the vector field of F (-y, 0) in the xy-plane. Be sure to draw enough vectors so that the pattern of the magnitude of the vectors and the direction of the vectors is clear. It is not required to label any points or vectors.

Sketch the vector field: F(x, y) = (1, 2y) Carefully draw at least four vectors in each of the four quadrants.

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

= xi + yj through the surface S, which is the part of the surface z = 36 – (x² + y2) above the disk of radius 6 Compute the flux of the vector field F centered at the origin, oriented upward. flux =

A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)

Cal 3