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 )
Squaring and adding, we get
cos2α + cos2 β + cos2 γ + cos2 δ
 = 1
3   [ (l + m + n )2 + (–l + m + n)2 ]  + (l – m + n)2 + (l + m –n)2]
 = 1
3  [ 4 (l2 + m 2 + n2 ) ]  = 3
4
          (as l2 + m 2 + n2 = 1)
Example 27 Find the equation of the plane that contains the point (1, – 1, 2) and is
perpendicular to each of the planes 2x + 3y – 2z = 5 and x + 2y – 3z = 8 Solution The equation of the plane containing the given point is
A (x – 1) + B(y + 1) + C (z – 2) = 0
Applying the condition of perpendicularly to the plane given in (1) with the planes