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.
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?