On one class of Lipschitz vector fields in a"e3

Under consideration are some continuous metric functions induced by one class of Lipschitz vector fields in a"e(3). These functions are showed to be quasimetrics within the domain of definition of the vector fields. We prove some analogs of the Rashevsky-Chow Theorem and the Ball-Box Theorem under some restriction on the class of vector fields. The methods of proofs do not use the existence of the nilpotent tangent cone.