Determine whether the following trajectories lie on a circle in R² or sphere in R³ 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.

r(t) = (√3 cos t + √2 sin t, -√3 cos t + √2 sin t, √2 sin t), for 0 ≤ t ≤ 2π