After introducing the scheme of zeros of a vector bundle which parametrizes the zeroschemes of its global sections, we give several alternative descriptions, Using results about symmetric algebras, we can characterize local properties of this scheme. If it has the expeted dimension, we say that the vector bundle has good sections. Examples show that manyinteresting bundles share this property which generalizes global generation. Finally, this notion is investigated further in the case of vector bundles of rank 3 on ℙ3.