Verified Solution • 2025–26 Session moderate

QJEEAdv17Ma5343: JEE Advanced 2017 Mathematics - Class 12 JEEAdv17Ma5343 Solution: The equation of the plane passing through the point (1, 1, 1)…

The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y −- 2z = 5 and 3x −- 6y −- 2z = 7 is

Multiple Choice Options

  • A 14x + 2y −- 15z = 1
  • B −- 14x + 2y + 15z = 3
  • C 14x −- 2y + 15z = 27
  • D 14x + 2y + 15z = 31

Step-by-Step Verified Solution

Let the equation of plane be ax + by + cz = 1. Then

a + b + c = 1

2a + b −- 2c = 0

3a −- 6b −- 2c = 0

⇒\Rightarrow a = 7b

c = 15b2{{15b} \over 2}

b = 231{{2} \over 31} , a = 1431{{14} \over 31} , c = 1531{{15} \over 31}

∴\therefore 14x + 2y + 15z = 31

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