Suppose that the path describes the position of the Starship Inertia at time t....

Suppose that the path

describes the position of the Starship Inertia at time t.

(a) Lt. Commander Agnes notices that the ship is tracing a closed loop. What is the length of this loop?

(b) Ensign Egbert reports that the Inertia’s path is actually a flow line of the Martian vector field F(x, y, z) = yi − 2xj + yk, but he omitted a constant factor when he entered this information in his log. Help him set things right by finding the correct vector field.