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- Find the flux of the constant vector field i = - 4i - 5j-2k through a square plate of area 16 in the zy-plane oriented in the positive r-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 =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 =
- Find the upward flux of F = (14e*, -7e, -6) through the first-octant part of the triangle x+2y+3z = 6. Answer: ECompute the flux of the vector field F = xi + yj through the surface S, which is the part of the surface z = 25 – (x2 + y?) above the disk of radius 5 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.)
- Find the curl of the vector field u = a) b) ▼xu =( V. (V x u) = = (7xyz², 6x² y³, 2x³ y³ z4 ).Sketch and describe the vector field F (x, y) = (-y,2x)Find the work done by the vector field (5x + yx, x² + 3 ) or the boundary of the rectangle 0 < x< 3,0 < y < 6|in the counterclockwise direction. a particle moving along (The force is measured in newtons, length in meters, work in joules=(newton-meters).) W = joules