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AP EAMCET202420 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The direction cosines of two lines are connected by the relations l+m-n=0 and l m-2 m n+n l=0 . If is the acute angle between those lines then =

Options

  1. A6
  2. B1 7
  3. C5 6
  4. D3

Correct answer

B. 1 7

Step-by-step solution

+m-n=0 n= +m m-2 m n+n =0 m-2 m( +m)+ (n+m)=0 ^2-2 m^2=0 =- 2 m, = 2 m n=(1- 2 ) m, n=(1+ 2 ) m : m: n=- 2 : 1:(1- 2 ) or 2 : 1: 1+ 2 Angle between these lines = |( 2 )(- 2 )+(1)(1)+(1- 2 )(1+ 2 )| 2+1+1+2-2 2 2+1+1+2+2 2 = |-2| 6-2 2 6+2 2 = 1 7

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