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JEE Main202127 Jul 2021Morning ShiftMathematicsThree Dimensional GeometryActual

Let the plane passing through the point - 1 , 0 , - 2 and perpendicular to each of the planes 2 x + y - z = 2 and x - y - z = 3 be a x + b y + c z + 8 = 0 . Then the value of a + b + c is equal to:

Options

  1. A3
  2. B8
  3. C5
  4. D4

Correct answer

D. 4

Step-by-step solution

The plane is normal to x - y - z = 3   &   2 x + y - z = 2 So, the normal of required plane is 2 i ^ + j ^ - k ^ × i ^ - j ^ - k ^ = i ^ j ^ k ^ 2 1 - 1 1 - 1 - 1 = - 2 i ^ + j ^ - 3 k ^ The required plane is passing through the point - 1 , 0 , - 2 . So, the equation of plane is - 2 x + 1 + 1 y - 0 - 3 z + 2 = 0 ⇒ - 2 x + y - 3 z - 8 = 0 ⇒ 2 x - y + 3 z + 8 = 0 So, a = 2 , b = - 1   &   c = 3 Hence, a + b + c = 4

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