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KCET2014MathematicsDeterminants

Lines ( x-2 1 + y-3 1 = z-4 -K ) and ( x-1 K = y-4 2 = z-5 1 ) are co-planar if

Options

  1. A( K =0 )
  2. B( K=-1 )
  3. C( K =2 )
  4. D( K =3 )

Correct answer

A. ( K =0 )

Step-by-step solution

Given equation, [ array l x-2 1 = y-3 1 = z-4 -K (1) x-1 K = y-4 2 = z-5 1 (2) array ] For co-planarity, we have [ array l | array ccc x₂-x₁ & y₂-y₂ & z₂-z₁ a₁ & b₁ & c₁ a₂ & b₂ & c₂ array |=0 | array cccc 1-2 & 4-3 & 5-4 1 & 1 & -K K & 2 & 1 array |=0 | array cccc 1 & 1 & 1 & -K K & 2 & 1 & =0 array |=0 array ]

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