

Tin: sin.\n.ni y./.vjf N 



Id between m, and w, if th- lines (1) ami 



re parall' .diculur. If these lines are 



parallel, tben $-0, un<l tl>* i. I..R- tan = 0; 



mm 



, 



i 



- 



ii is tin* condition that lim* (1) an re paral 



condition i> also evident from a mere inspection of 

 equations (1) and (2). 



If the linrs , 1 , .nid (2) (Art. 61) are perpendicular, then 

 + U0 and tan - oo , 



^ 

 1 -f 



which is the condition tli.it ( 1 > and (2) are perpendicular. 

 So also from [1 ">] the lines 



.l.r + J?iy+ C t and ^4>r -|- 4 + C, 

 parallel if (and only it > A.B^-A^B^^ 

 if I //, = X, : B, ; 



they are perpendicular if ( and .nl\ I t.. + B|B t sO, 



if ^rB^-B,:^ 



The condition just found enables one to write down readily 

 tj nations of lines that are parallel or perpendicular to 

 given lines, and which also pass through given points. 



It must not be foigotten that thta oooclorion b drawn only for UMI 

 that are NO* perpendicular to the x-axi ; beeauee If the line* are perpen- 

 dicular to the **xiii then equatkws (1) and (S) are laappUcable (of. Art. 60). 



