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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

The direction cosines of the lines connected by the relations 1+m+n=0,21 m+2 - mn =0 is/are

Options

  1. A( 1 3 , 1 3 , 1 3 )
  2. B( 1 6 , 1 6 ,- 2 6 )
  3. C( 1 6 ,- 2 6 ,- 1 6 )
  4. D(- 1 3 ,- 1 3 , 1 3 )

Correct answer

C. ( 1 6 ,- 2 6 ,- 1 6 )

Step-by-step solution

Given lines are + m + n =0 ....(1) 2 m+2 n-m n=0 ....(2) Putting the value of n from (1) in (2), we get 2 ~m +2 -( + m ) - m -( + m ) =0 n =-( + m ) aligned & m ^2+ m -2 ^2=0 & ( ~m f )^2+ ( m )-2=0 & ~m f =- 1 1+8 2 =- 1 9 2 =- 1 3 2 & ~m =-2.1 aligned If m f =-2 if m =1 Then n =-( -2 )= n =-(2 ) m -2 = 1 = n 1 m l = 1 = n -2 Direction cosines are - ( 1 6 ,- 2 6 , 1 6 ): ( 1 6 , 1 6 ,- 2 6 )

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