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JEE Main202124 Feb 2021Evening ShiftMathematicsThree Dimensional GeometryActual

Let a , b ∈ R . If the mirror image of the point P a , 6 , 9 with respect to the line x - 3 7 = y - 2 5 = z - 1 - 9 is 20 , b , - a - 9 , then | a + b | is equal to:

Options

  1. A86
  2. B90
  3. C84
  4. D88

Correct answer

D. 88

Step-by-step solution

P a , 6 , 9 x - 3 7 = y - 2 5 = z - 1 - 9 Q = 20 , b , - a - 9 Mid point of P Q = a + 20 2 ,   b + 6 2 ,   - a 2 lies on line 20 + a 2 - 3 7 = b + 6 2 - 2 5 = - a 2 - 1 - 9 a + 20 - 6 14 = b + 6 - 4 10 = - a - 2 - 18 14 + a 14 = b + 2 10 = a + 2 18 a + 14 14 = a + 2 18 18 a + 252 = 14 a + 28 4 a = - 224 a = - 56 b + 2 10 = a + 2 18 b + 2 10 = - 54 18 b + 2 10 = - 3 ⇒ b = - 32 | a + b | = | - 56 - 32 | = 88

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