Question
Find equation of a plane parallel to 2x – 3y + z + 9 = 0 and also passing through origin.
Solution
Equation of any plane parallel to the plane
2x – 3y + z + 9 = 0 is
2x – 3y + z + k = 0 ..(1)
∴ it passes through origin (0, 0, 0)
∴ 0 – 0 + 0 + k = 0 ⇒ k = 0
Putting k = 0 in (1), we get,
2x – 3y + z = 0
which is required equation of plane.
