1 1 l^rpendifular plan**. If the plane* (1) and (2) are 



perj r.i.-li other, then cos0 0, 



ui,.l ^ f + Ji,Ji tf + f|Cf 0| . . . [24] 



220. Distance of r. point from a plane. Lai 



*i"0*fktO 



be a given point, and 



D-Q . . . (1) 



a given plane. The perpendicular distance of J\ from the 

 plane is equal to t ! distance from the plane (1) to a parallel 

 plane through tin- i><int , /., .. in equal to t 



lengths of the normals, from the origin, to these two 

 parallel planes. 



The parallel plane through P l has for its equation by 

 Art. 219, equation (8), 



Ax+By + ft- Ar l ^By l ^Cx l . . . . 



By [-J1 ]. the lengths of the normals to planes (1) and 

 are, respectively, 



-D 



I =p' p be the required distance, 



-f I> 



r.,., 



In formula [25], the sign of the radical is taken opposite 

 to the sign of D (Art. 218) ; and the sign of d shows on 

 which side of the given plane lies the given point. 



II. THE STRAIGHT Lore 



22L Two equations of the first degree represent a straight 

 line. Every equation of first degree represents a plane 



