Question
Find the equation of plane passing through origin and intersection of planes 2x – 3y + z = 9, x – y + z = 4
Solution
The equation of any plane through the intersection of planes
2x – 3 y + z – 9 = 0 and x – y + z – 4 = 0 is
(2 x – 3 y + z – 9) + k (x – y + z – 4) = 0 ...(1)
∴ it passes through origin (0, 0, 0,)
∴ (0 – 0 + 0 – 9) + k (0 – 0 + 0 – 4) = 0
Putting 
or 4 (2x – 3 y + z – 9) – 9 (x – y + z – 4) = 0
or 8 x – 12 y + 4 z – 36 – 9 x + 9 y – 9 z + 36 = 0
or – x – 3 y – 5 z = 0
or x + 3 y + 5 z = 0, which is required equation of plane.
