////. /'.*/\ y ;N 



; yector makes with tin* on.nlmate axes, respectively. TbeM 

 angles are called the direction angles of tin 1 "/ 



direction cosines. The point may be con- 

 | ciaely len..t,-.l a.s tin- point /'s(p, , 0, y). 



onnect these coordinate* with tho* 

 rectangular system ; for, projecting OP upon the axes 



' 



0-pess*, y = p*M, * = peMv [3] 



1 also, pJ ^-f^-f* 1 , as in equation** [ *J ] . 

 Moreover, th.- -u cosines are not in.l.-jN-M'l.-m, Imt 



an- fonnrt-trd l.v an r.|ii,iti.n ; l'>r, \>\ OOmhinillg t:..- 



=1. . . [4] 



i relation was to have been expe< OS only 



o magnitudes are necessary t<> .l.-t.-nnin.- tic- j. 



point, ami tln-n-foir t: - p, , & 7 riuli 



Any three iiiinilx : . are proportional to the <lirec- 



i cosines of some line : l>ecause if these numbers are con- 

 .red as the roonlinates f a point, then the ilin 



nt" the : that |H)illt are. li\ 'j. [ .',], 



:-n cosines are proportional to and are 



fouinl liy li\iilin^ ' -pertiv.-h, ly the same constant, 



reel ion cosines are useful in giving the direct ion of any 

 line in space. The direction of any line is the same as 



1 line thr.Mi-li t 

 i of a line may be given by the direction angles of some 



