$4.-$ The Lagrangian $($dimensionless$)$ description of the motion of a body is defined by:

$x_1={}_1-2t{}_2$;$,x_2=t{}_1+(1-t){}_2$;$,x_3={}_3$

a$)$ Determine the Eulerian description of this movement.

b$)$ Write the velocity and acceleration fields, both Lagrangian and Eulerian.

c$)$ Determine the trajectory of the particle that at time $t=1$ is at point $P(1,2,0).$