-I ) 



SOLID GEOMETRY. 



I. Strait/ ft f Ll, t fl and Plane. 



1060. The co-ordinates of four points are a - b, a-c, a - <1 ; 

 b-c, b-d, 6-a; c-<7, c-a, c-b; d-a, d-b,d-c; r< 



liatthe straight line, joining the middle points of 

 any two opposite edges of the tetrahedron of which they are the 

 angular points, passes through the origin. 



106K Of the three acute angles which any straight lino 

 makes with three rectangular axes, any two are together gr 



than the third. 



10G2. The straight line joining the points (a, b, c), (a', &', c',) 

 will pass through the origin if 



aa + bb' + cc = pp', 



p, p' being tho distances of the points from the origin, and tliu 

 axes rectangular. Obtain tin- oorreeponduig equation wlu-n tho 

 axes are inclined respectively at angles a, /?, y. 



10G3. Fron. /'.V ]MT].'ii(li.-nlar 



to the planes of sx, y, is the origin, and a, /?, y, tho angles 

 \vhi.-h OP makes with the axes (rectangular) and with th- plan.- 

 : ],rovethat 



, 1 



" 



, 

 810*0 sin*/? sin'y 



10G4. The equations of a straight line b< D in the 



. a -f ma nyb + nx 



J - ~ 



