The question statement is:

A particle moves in a space following the trajectory r(t). Suppose that r'' = ||r||^2 * r for all t, r(0) = <1, 1, 1> and r'(0) = <1, 2, 5>. Define L = r(t) X r'(t).

a) show that L is constant and finds its value

Am I allowed to just that r(0) X r'(0)?

Or do I have to somehow work backwards and solve for r(t) and r'(t)?

and how would I show that L is constant?