There are a lot of questions in my (first year) lecture notes where the instructor uses moment of inertia tensor to perform calculations involving angular momentum. And he directly makes a statement such as Ixy =0 ... I have no idea how he reached that conclusion just by observing and neither does he clarify one bit.
Is there any symmetry consideration to be taken into account? I know that say, if an object lies in the xz plane its product of inertia Ixy and Iyz will be zero but how to know that for the image file I've uploaded?
Here the only term that remains in calculation is Izx while all of Ixx , Iyy , Izz , Iyz , Ixy turn out to be zero. HOW??