Nice Vectors

I wanted to be nice this semester in computer graphics. In my exercises, I ask students to do a lot of 3D vector math. These vectors must often be normalized, which means their magnitude is 1: $$\begin{align} \sqrt{a^2 + b^2 + c^2} &= 1 \\ \end{align}$$ If that's the case, so is their squared magnitude: $$\begin{align} a^2 + b^2 + c^2 &= 1 \\ \end{align}$$ I needed vectors for which this equation…