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COMEDK2023MathematicsThree Dimensional Geometry

If two lines L₁: x-1 2 = y+1 3 = z-1 4 and L₂: x-3 1 = y-k 2 =z intersect at a point, then 2 k is equal to

Options

  1. A9
  2. B1 2
  3. C9 2
  4. D1

Correct answer

A. 9

Step-by-step solution

Let x-1 2 = y+1 3 = z-1 4 = Now, any point P that lies on the lines L₁ has the form (1+2 ,-1+3 , 1+4 ) . Now, on putting x=1+2 , y=-1+3 and z=1+4 into the equation of lines L₂ , we get aligned & 1+2 -3 1 = -1+3 -k 2 =1+4 & 1+2 -3 1 =1+4 & -2 =3 = -3 2 & -1+3 -k 2 =1+4 & -1+3 -k=2+8 & -5 =3+k & -5 (- 3 2 )=3+k [ =-3 / 2] & k= 15 2 -3 & k= 9 2 & 2 k=9 & aligned

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