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The equation of plane which passes through the point (2, -3, 4) and is parallel to the plane 2x - 5y - 7z = 6 is

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  1. 2x - 5y - 7z - 9 = 0
  2. 2x - 5y - 7z + 6 = 0
  3. 2x - 5y - 7z + 9 = 0
  4. 2x - 5y - 7z - 6 = 0

Answer (Detailed Solution Below)

Option 3 : 2x - 5y - 7z + 9 = 0
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Detailed Solution

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The equation of a plane parallel to the given plane is →

2x – 5y – 7z + λ = 0     …i)

The plane will pass through the (2, -3, 4) if

2 × 2 – 5 × (-3) – 7 × 4 + λ = 0

⇒ 4 + 15 – 28 + λ = 0

⇒ λ = 28 – 19 = 9

Pulting the value of λ = 9 in eqn. i) we get →

2x – 5y – 7z + 9 = 0

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Q1.The equation of plane which passes through the point (2, -3, 4) and is parallel to the plane 2x - 5y - 7z = 6 is

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