Answered>Order 3950

The flow lines ( or streamlines ) of a vector field are the paths followed by a particle whose velocity field is the given vector field. Thus, the vectors in a vector field are tangent to the flow lines. See attached file for full problem description.The flow lines (or streamlines ) of a vector field are the pathsfollowed by a particle whose velocity field is the given vector field.Thus, the vectors in a vector field are tangent to the flow lines.Consider the vector field F(x,y,z) = ?5y, 5x, ?2z?. Show that r(t) = ?e5t + e?5t, e5t ? e?5t, e?2t? is a flowline for the vector field F. .That is, verify that (I trust you here) r?(t) = F(r(t)) =Now consider the curve r(t) = ?cos(5t), sin(5t),e?2t?. It is not a flowline of the vector field F, but of a vector field G which differs in definition from F only slightly. only slightly. .G(x,y,z) = ? , , ?.