Planes of symmetry of a molecule Are we limited to use only xy, yz and zx planes to check for planes of symmetry of a molecule? Because I see a plane of symmetry in  the following molecule through the two shown H atoms or OH groups. I am aware of the 3D structure shown by this projection. And since this molecule is Chiral, and has enantiomeric mirror image, this existence of a plane of symmetry appears contradictory.
I don't see planes of symmetry through H atoms or OH groups. Actually, these planes are not present. It is easy to check this by looking at the position of the CH3 group after reflection in one of these planes: you find CH3 at a completely different position (none of the original positions is mapped and hence you can distinguish the starting configuration from the final one).