A rigid body consists of six particles, each of mass m, fixed to the ends of three light rods of length 2a, 2b and 2c, respectively, the rods being held mutually perpendicular to one another at their midpoints. 

(a) Show that a set of coordinate axes defined by the roods are principal axes and write down (15) the inertia tensor for the system in these axes.
(b) Use matrix algebra to find the angular momentum and kinetic energy of the system when (10) it is rotating with angular velocity ~ω about an axis passing through the origin and the point (a, b, c)