tend to be equal, as well as perpen- dicular whenever and just when the sum of the products of the path cosines is zero. Proof The condition with regard to parallelism follows from the fact that each lines will be parallel to and agree in direction with the same line through the source whenever and just whenever their own direction angles are equal. The condition with regard to perpendicularity follows from (V), with regard to if Turbulence training ^ = — , after that cos Five Equals 0, and on the other hand queen.at the.d. Li - They'll be similar and have reverse directions when and just when the path angles tend to be extra. capital t 2 lines within space have been demonstrated to be perpendicular once the angle together is --, but the outlines do not really intersect. 242 Brand new ANALYTIC GEOMETRY Within the programs we usually have given not the actual direction cosines, but three numbers to which they are proportional. Hence the importance of the next Corollary. When the direction cosines of 2 lines are proportional to some, h, Grams as well as a\ h\ c', then^the problems for pa^'allelism as well as pteipendicularity are correspondingly http://www.cheap-jerseys-sale.com