A vector method for the determination of trajectory parameters of a meteor in the Earth's atmosphere and its heliocentric orbit elements is developed. The geocentric rectangular coordinate system is used as the main one, which allows us to avoid some inaccuracies and carry out all the calculations easier. The method is largely targeted for the application to the results of TV observations of meteors with taking into account possibilities of the modern digital processing and algorithm languages, but it can be used for other observational methods as well The method enables one to take into account such features of the digital processing of TV observations of faint meteors as their short angular length, few amount of points with coordinates of a meteor head and known time moments determined by TV tube frame rate, which complicates the velocity calculation, and, at the same time, the great overall number of measured points along a meteor trail, which simplifies more accurate radiant calculations.