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 the sphere with center at the origin. 2. Relevant equations I know dot product might help: r(t) . r'(t) = 0 and the equation of a sphere in 3-space: r2 = x2 + y2 + z2 3. The attempt at a solution if I write out the components of the dot product... r(t) . r'(t) = fx(t)*fx'(t) + fy(t)*fy'(t) + fz(t)*fz'(t) = 0 From there, I am not sure what to do, if that even is the right way to start.