,
3
1
, 
3
1
,  
3
1
B(0, , 0)
 a  
C(0, 0, )
a
a( , 0, )G
a
F(0, , )
a a
X
D( , , 0)
a
a
Y
Z
O
Fig 11 21
© NCERT
not to be republished
THREE D IMENSIONAL G EOMETRY
495
Similarly, the direction cosines of AF, BG and CD are –1
3
, 
3
1 , 
3
1 ; 
3
1 ,
–1
3
, 
3
1   and  
3
1  , 
3
1 , –1
3
, respectively Let l, m, n be the direction cosines of the given line which makes angles  α, β, γ, δ
with OE, AF, BG, CD, respectively Then
cosα  = 1
3
 (l + m+ n); cos β = 
1
3 (– l + m + n);
cosγ =
1
3
(l – m + n); cos δ = 
1
3 (l + m – n)     (Why