THE PLANE 78 



2-414 



cos a - - -- 0-4828 

 5 



a=618 / 



2-414 



cos Q = = 0-8047 

 o 



P = 36 25' 



2-414 

 cos v = - = 0-3449 



7 



y = 69 50' 



The plane makes angles 29 52', 53 35', and 20 10' with the 

 axes OX, OY, and OZ respectively. 

 If x lt y lt z l are the co-ordinates of P 



2 



Then x l =4 = 1-168 

 5 



fl 2 

 yi = L. = 1-943 



V z 

 z =Z. = 0-8328 



7 



46. To find the perpendicular distance of a given point from a 

 given plane. 



X tl % 



Let- + r + -= 1 be the equation to the plane. Then if p 

 a o c 



is the perpendicular distance from the origin to the plane, and 

 I, m, and n are the direction cosines of that perpendicular 



V V V 



Then I = -, m = y, and n = - 



a o c 



Hence Ix + my + nz = p will be the equation to the plane, and 

 1 



Let x lt y lt z l be the co-ordinates of the given point, and through 

 this point let a plane be drawn parallel to the given plane. 

 Since the two planes are parallel, the perpendiculars drawn to 

 these planes will be parallel, and will therefore have the same 

 direction cosines. 



Hence Ix + my + nz = p l will be the equation to the parallel 

 plane, where p t is the perpendicular distance from the origin to 

 the plane. 



Also lx l + my 1 + nz l = p^, since the plane passes through the 

 point whose co-ordinates are (x lt y v z^). Now p p is the dis- 





