Determine whether the vector field is conservative and, if so, find the general potential function. = +c F = (cos z, 2y¹7, —x sin z) Note: if the vector field is not conservative, write "DNE".
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- 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-x²-2², y 20, and oriented in the positive y-direction. (Use symbolic notation and fractions where needed.) 1.45-1 yasThe angular velocity vector, ω, can be obtained by adding all components of the angular velocities or byA. taking half of the Laplacian form of the vector v.B. taking half of the curl of vector v.C. taking the gradient of vector v.D. solving for the cross product of the vector field and the gradient of v.Which of the figures below shows a direction field for dy ? dx
- Find u · (v ✕ w).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 = (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) V. dS =Which of the following equations would produce the direction field above? dy = 1 y da O dy dr =x-Y dy = x² y da dy - ² y da 1