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Let the lines L₁ and L₂ be given by L₁: x+2 2 = y+3 1 = z-b -1 and L₂: x 1 = y+7 a = z 2 intersect at a point P . If a line L₃ passing through the point (3, -3, 5) and parallel to the vector i - 2 j + k also passes through the point P , then the value of a + b is equal to :

Options

  1. A5
  2. B3
  3. C9
  4. D18

Correct answer

C. 9

Step-by-step solution

The equation of the line L₃ passing through (3, -3, 5) and parallel to i - 2 j + k is: x-3 1 = y+3 -2 = z-5 1 = t Any point on L₃ is of the form (3+t, -3-2t, 5+t) . Since L₃ passes through the intersection point P of L₁ and L₂ , this point must lie on L₁ for some value of t . Substituting the coordinates into the first two terms of L₁ (which do not contain unknowns): (3+t)+2 2 = (-3-2t)+3 1 t+5 2 = -2t t+5 = -4t 5t = -5 t = -1 Substituting t = -1 , the coordinates of the intersection point P are (2, -1, 4) . Since

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