(a)
7x + 5y + 6z + 30 = 0 and 3x – y – 10z + 4 = 0
(b)
2x + y + 3z – 2 = 0
and x – 2y + 5 = 0
(c)
2x – 2y + 4z + 5 = 0
and 3x – 3y + 6z – 1 = 0
(d)
2x – y + 3z – 1 = 0
and 2x – y + 3z + 3 = 0
(e)
4x + 8y + z – 8 = 0
and y + z – 4 = 0
14 In the following cases, find the distance of each of the given points from the
corresponding given plane Point
Plane
(a)
(0, 0, 0)
3x – 4y + 12 z = 3
(b)
(3, – 2, 1)
2x – y + 2z + 3 = 0
(c)
(2, 3, – 5)
x + 2y – 2z = 9
(d)
(– 6, 0, 0)
2x – 3y + 6z – 2 = 0
Miscellaneous Examples
Example 26 A line makes angles  α,  β, γ and  δ with the diagonals of a cube, prove that
cos2 α + cos2 β + cos2 γ + cos2 δ = 4
3
Solution A cube is a rectangular parallelopiped having equal length, breadth and height Let OADBFEGC be the cube with each side of length a units