AN.u.Y in i;i-:tt.Mi-:THY 



[CM. I. 



: whose radius vector is parallel to the line. Sometimes, 

 as an equivalent conception, it is convenient to consider t In- 

 direction angles as those formed by tin; line with three lines 

 which pass through some point of the ^iven line, ami 

 parallel, respectively, to the coordinate axes. 



204. Distance and direction from one point to another ; rec- 

 tangular coordinates. A few elementary problems coneerninir 



points can now be easily solved ; 

 for example, the problem of find- 

 ing the distance between : 

 points. Let OX, OY, OZ be 

 a set of rectangular axes, ;md 



A=(^ryr z i) antl ^2=( 



be two Driven points. Then the 



planes through P l and P T paral- 

 lel, respectively, to the coordi- 

 nate planes, form a rectangular 



parallelepiped, of which the required distance PiP% is a 



diagonal. From the figure, 



since Z P^QP^ = 90 and Z MJRMJ = 00, 



therefore IP = P~ + QP?=MJMf + QP? 



+ i- QP? 



- ^i) 2 + (y, - ytf + (z, - gj*. 



Tli at is, if d be the required distance, 



Fio. 144. 



Moreover, since the direction of the line PP^ is given l.v 

 the angles 0,^,7. which it makes, respectively, with the : 



jZ', drawn through P 1 pantile! to thu 



