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MHT CET2018MathematicsThree Dimensional Geometry

If planes r → . ( p i ^ − j ^ + 2 k ^ ) + 3 = 0 and r → . ( 2 i ^ − p j ^ − k ^ ) − 5 = 0 include angle π 3 then the value of p is

Options

  1. A1 , − 3
  2. B- 1 , 3
  3. C- 3
  4. D3

Correct answer

D. 3

Step-by-step solution

cos ( π 3 ) = ( 2 p + p − 2 p 2 + 5 p 2 + 5 ) 1 2 = ( 3 p − 2 p 2 + 5 ) p 2 + 5 = 6 p − 4 p 2 − 6 p + 9 = 0 ( p − 3 ) 3 = 0 p = 3

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