74 PRACTICAL MATHEMATICS 



tance between these two parallel planes, and this will also be the 

 perpendicular distance of the given point from the given plane. 



Then p^ p = Ix 1 + my l + nz l p 



(X-, II* 2, 1 



, + TT + - l \ 



{ a b c J 



b 2 c 2 



Example. Find the perpendicular distance from the point 

 whose co-ordinates are (8, 3, 7) to the plane whose equation is 

 I5x 9t/ + 5z = 45. 



fv\ aj jy 



Then - | + - = 1 will be the equation to the plane where 

 359 



3, 5, and 9 are the intercepts. 

 The perpendicular distance = 



8_ 3 7__ 

 ~ + ~ 



/i u J_ JL 

 V9" 1 25 + 81 



83 



A/331 

 = 4-562 

 47. To find the angle between two planes. 



/}J 7/ 2J OC *U Z 



Let -- h -T- H -- = 1 and -- H-f-H -- =1 be the equations 



a i "i c i a z "?. c z 



to the planes. 



Then for the first plane l v x + m^y + n^z = p lt where 



1 L = l, m = s f and Wl = l 



a c 



111 



These relations give the direction cosines of the perpendicular 

 to the plane. 



For the second plane l^x + m^y + n z z = p z , where 



c 



