UPSC NDA Math Model Paper 7

Given: Equation of plane 5x - 6y + 7z = 3 ⇔ 5x - 6y + 7z - 3 = 0
Equation of a plane parallel to a given plane 5x - 6y + 7z - 3 = 0 is 5x - 6y + 7z + λ = 0
Plane is passing through the point (2, 3, 4)
So, point (2, 3, 4) satisfy the equation of plane 5x - 6y + 7z + λ = 0
⇒ (5 × 2) - (6 × 3) + (7 × 4) + λ = 0
⇒ 10 - 18 + 28 + λ = 0
⇒ 20 + λ = 0
∴ λ = -20
So, Equation of plane is 5x - 6y + 7z - 20 = 0