1. The problem statement, all variables and given/known data Let r1 and r2 be differentiable 3-space vector-valued functions. Show that for a differentiable 3-space vector-valued function r, the graph of r lies on a sphere centered at the origin if and only if r(t) and r′(t) are orthogonal (perpendicular) for all t. 2. Relevant equations Dot products? 3. The attempt at a solution If R(t) is on the surface of such a sphere then ||R(t)||=C, is constant.