  The new Gaia data release (EDR3) with improved astrometry has opened a new
era in studying our Milky Way in fine detail. We use Gaia EDR3 astrometry
together with 2MASS and WISE photometry to study two of the most massive
molecular clouds in the solar vicinity: Orion A and California. Despite having
remarkable similarities in the plane of the sky in terms of shape, size, and
extinction, California has an order of magnitude lower star formation
efficiency. We use our state-of-the-art dust mapping technique to derive the
detailed three-dimensional (3D) structure of the two clouds, taking into
account both distance and extinction uncertainties, and a full 3D spatial
correlation between neighbouring points. We discover that, despite the apparent
filamentary structure in the plane of the sky, California is a flat 120-pc-long
sheet extending from 410 to 530 $pc$. We show that not only Orion A and
California differ substantially in their 3D shapes, but also Orion A has
considerably higher density substructures in 3D than California. This result
presents a compelling reason why the two clouds have different star formation
activities. We also demonstrate how the viewing angle of California can
substantially change the cloud's position in the Kennicutt-Schmidt relation.
This underlines the importance of 3D information in interpreting star formation
relations and challenges studies that rely solely on the column density
thresholds to determine star formation activities in molecular clouds. Finally,
we provide accurate distance estimates to multiple lines of sight towards
various parts of the two clouds.
