Question
Find the distance between parallel planes:
2x – y + 3z – 4 = 0 and 6x – 3y + 9z + 13 = 0.
Solution
The equations of given planes are
2x – y + 3 z – 4 = 0 ... (1)
and 6 x – 3 y + 9 z + 13 = 0 ....(2)
Let (x1, y1 , z1 ) be any point on plane (1)
∴ 2 x1 –y1 + 3 z1 – 4 = 0 or 2x1– y, + 3 z1 =4 . (3)
Length of perpendicular from (x1, y1 , z1 ) to the plane (2) is
which is required distance between the planes.
