7.1 THE / 8? ACM -ill 



is clear, by reasoning sjiiinl.tr to that .f Art. 75, i'ai 



.11* [13], [14],nn<l [ !.*.]. neither 



aeparately nor iu cumhin.itiMM, can alter the degree of an 

 equation to which they may be applied. 



EXAMPLES ON CHAPTER I 



1 rroro that the triangle formed by Joining the potato (I, 9; S), 

 (8, 3, 1), and ( in pain, U equilateral. 



2. Tl>e direction cosines of a straight line are proportional to 1, 2, 8 1 



3 1 . i i he angle between two straight liuee whose direction cosines 

 are pro|K>rtional to 9 . respectively. 



tie rectangular cotfrdinatea of a point are (A 1, 9 VI); and 



. .. . . 



3. The polar coordinate* of a point are (.1, -, *); find iU rectan- 

 gular coordinates. 



xpraet the distance between two point* in terms of their polar 

 coordinates. 



7 1 ! the coordinates of the point* diriding the line from 



2, 4) externally and internally in the ratio 2:S. 

 8. \ .,. kmgth of a line whose projections on the coordinate 



ax.-< :ir- J, 1, ,i. i'->i- -.-ti\. !\ V 



9 1; I the radius vector, and its direction cosines, for each of the 

 '.(1. 1. _). (.1.0.6). 



10. Fin.l th.- r.Mit.-r of -i.ivitv .f the triangle of Ex. 1. 



11. Kin.l the direction angles of a straight line which makes equal 

 angles with the three coordinate axes. 



12 A straight line makes the angle 30 with the *axia, and 79* 

 he *axis. At what angle doe* it meet the yaxtsT 



13. Prove analytically that the straight line* Joining the mid-| 



of tho opposite edges of a tetrahedron pass through a common point, 



a:> 1 ar.- bisected > It 



14. Prove a , that the straight lines joining the mid-point* 

 of the oppoaite sides of any quadrilateral pass through a common point, 

 and are bisected b\ 



See Ex. 16, p. * 



