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JEE Main2013MathematicsStraight LinesActual

If two lines L₁ and L₂ in space, are defined by aligned & L₁= x= y+( -1), & z=( -1) y+ and & L₂= x= y+(1- ), aligned z=(1- ) y+ then L₁ is perpendicular to L₂ , for all nonnegative reals and , such that :

Options

  1. A+ =1
  2. B+ =0
  3. C=

Correct answer

3

Step-by-step solution

For L ₁ , aligned & x= y+( -1) y= x-( -1) & z=( -1) y+ y= z- -1 aligned From (i) and (ii) x-( -1) = y-0 1 = z- -1 The equation (A) is the equation of line L ₁ . Similarly equation of line L ₂ is x-(1- ) = y-0 1 = z- 1- Since L ₁ L ₂ , therefore aligned & +1 1+( -1)(1- )=0 & + =0 =- & = aligned

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