Let r(t) be a nice vector-valued function of 1 variable over the real line (so that we can take the derivative of each component as many times as we want). Show that if r(t).r'(t) = 0 ( the dot product of r(t) and r'(t) equals to zero) for every t, then

/r(t)/ = /r(0)/ for every t

That is, /r(t)/ must be a constant function.