SOLID GEOMKTKV. 



1069. A straight line always intersects at right angles the 

 line 



x + y = z = 0, 



and also intersects the curve 



y 0, x 9 = az : 

 prove that the equation of its locus is 



x* - y* = az. 



1070. The equations 



ax '. c'x + by + a'z b'x + ay -4- cz 



x y z 



represent in general three straight lines mutually at right angles ; 

 but, if 



b'c __ , c'a' _ 



they represent a plane and a straight line perpendicular to that 

 plane, 



1071. The two straight lines 



~ cos a ~~ * 

 the axis of x in 0, & \ and P, P f are points on the two such 



(1) OP = k(> 

 (2) 

 (3) 

 prove that the equ; i /"is 



(1) (a; + a) (y sin a + z cos a) - k (x - a) (y sin a - z cos a) ; 







= -(*-); 



W /wt /. *in n ft v '' 



cos a sin a 

 being taken on the same side of the plane y. 



