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MHT CET2018MathematicsThree Dimensional Geometry

If planes x - c y - b z = 0 , c x - y + a z = 0 and b x + a y - z = 0 pass through a straight line then a 2 + b 2 + c 2 =

Options

  1. A1 - a b c
  2. Ba b c - 1
  3. C1 - 2 a b c
  4. D2 a b c - 1

Correct answer

C. 1 - 2 a b c

Step-by-step solution

Since the given planes pass through a straight line ⇒ | 1 − c − b c − 1 a b a − 1 | = 0 ⇒ 1 ( 1 − a 2 ) + c ( − c − a b ) − b ( a c + b ) = 0 ⇒ 1 − a 2 − c 2 − a b c − a b c − b 2 = 0 ⇒ 1 − 2 a b c − a 2 − b 2 − c 2 = 0 ⇒ 1 − 2 a b c = a 2 + b 2 + c 2

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