Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If a curve has the property that the position vector $\vec{r}(t)$ is always perpendicular to the tangent vector $\vec{r'}(t)$, how can I show that the curve lies on a sphere with center the origin?

This is a problem from J. Stewart's book, but I'm stuck, so any tip will be helpful

Thanks in advance

share|cite|improve this question
Remember that $|v|^2=\langle v,v\rangle$, this with the camareon's answer solve you problem (You have to derivate your function). – DiegoMath Jun 21 '14 at 18:09
up vote 5 down vote accepted

Hint: $\vec{r}(t)\cdot\vec{r}\,'(t) = \dfrac{1}{2}\dfrac{d}{dt}(\vec{r}(t)\cdot\vec{r}(t))$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.