1. The problem statement, all variables and given/known data http://i.imgur.com/6j8W6.jpg I'm trying to understand that example in the text. I can imagine a curve on a sphere having the derivative vector being orthogonal to the position vector. What I don't understand is, how does "if a curve lies on a sphere with center the origin" mean the same thing as "if |r(t)|=c (constant)"? 2. Relevant equations The problem is I don't understand why the statement says "Show that if |r(t)|=c ..." Doesn't the example mean that every derivative vector of a curve is orthogonal to the position vector since |r(t)|=c for all t as long as the curve is continuous? (thinking it in terms of sqrt(x^2+y^2+z^2)) When is |r(t)| not equal to a constant?