Do Carmo's book on "Differential geometry of curves and surfaces" has a problem that I can't find the answer of. It is on page 5(1st exercise problem#2) is:

Let be a parametrized curve which does not pass through the origin. If is the point of the trace of closest to the origin

and , show that the position vector is orthogonal to .

Here is the derivative of at .

How do I prove this? Is it possible to give some hints?