1. The problem statement, all variables and given/known data if a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t). show that the curve lies on a sphere with center the origin. 2. Relevant equations 3. The attempt at a solution I'm not quite sure how to prove this. I can write r'(t)[itex]\bullet[/itex]r(t)=0 but expansion doesn't yield anything seemingly useful. What direction should I look in?