Chapter 14.3, Problem 29E

Trajectories on circles and spheres Determine whether the following trajectories lie on a circle in ${ℝ}^2$ or sphere in ${ℝ}^3$ centered at the origin. If so, find the radius of the circle or sphere and show that the position vector and the velocity vector are everywhere orthogonal.

25. r(t) = 〈8 cos 2t, 8 sin 2t〉, for 0 ≤ t ≤ π