Using accelerometers I have acquired two $3D$ vectors $V_1$, $V_2$ which both have $(x, y, z)$.
Assume that these vectors are points ($P_1$ and $P_2$) on the surface of a sphere ($S$), so that the vector is perpendicular to the surface. Also assume that $P_1$ and $P_2$ are on the same hemisphere of the surface. The distance between $P_1$ and $P_2$ is static: $d=0.2m$.
How do I calculate the radius/diameter of the sphere?
In context: two accelerometers provide the data for $V_1$ and $V_2$. They are positioned on the chest ($P_1$ and $P_2$), the chest is the sphere, the distance between the accelerometers ($d=0.2m$) is static and breathing causes the accelerometers to 'rotate' (and thus changing the vectors).