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AP EAMCET20228 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

If the direction cosines of a line satisfy the relations l-m+n=0 and l m+m m-4 n l=0 , then the direction cosines of the line are

Options

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

Correct answer

D. ( 1 6 , 2 6 , 1 6 )

Step-by-step solution

l, m and n are the direction cosines of any line l^2+m^2+n^2=1 ...(i) Given, l-m+n=0 aligned & l=m-n and l m+m n-4 n l=0 & (m-n) m+m n-4 n(m-n)=0 & m^2-m n+m n-4 m n+4 n^2=0 & m^2+4 n^2-4 m n=0 (m-2 n)^2=0 & m=2 n l=2 n-n=n aligned From Eq. (i), n^2+4 n^2+n^2=1 n= 1 6 , m= 2 6 , l= 1 6 Direction cosines are ( 1 6 , 2 6 , 1 6 ) and (- 1 6 ,- 2 6 ,- 1 6 ) .

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