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The equation of the line which intersect each of the two lines 2 x + y - 1 = 0 = x - 2 y + 3 z and 3 x - y + z + 2 = 0 = 4 x + 5 y - 2 z - 3 = 0 and is parallel to x 1 = y 2 = z 3 is

Options

  1. A4 x + 7 y - 6 z -1 = 0 = 2 x - 7 y + 4 z +3
  2. B4 x + 7 y - 6 z - 4 = 0 = 2 x - 7 y + 4 z + 2
  3. C4 x + 7 y - 6 z - 3 = 0 = 2 x - 7 y + 4 z +7
  4. D4 x + 7 y - 6 z + 7 = 0 = 2 x - 7 y + 4 z - 3

Correct answer

C. 4 x + 7 y - 6 z - 3 = 0 = 2 x - 7 y + 4 z +7

Step-by-step solution

Equation of the first plane is 2 x + y - 1 + λ x - 2 y + 3 z = 0 ⇒ x 2 + λ + y 1 - 2 λ + 3 λ z - 1 = 0 Equation of the second plane is 3 x - y + z + 2 + u 4 x + 5 y - 2 z - 3 = 0 ⇒ x 3 + 4 u + y - 1 + 5 u + z 1 - 2 u + 2 - 3 u = 0 Required line must lie in both planes and parallel to the line x 1 = y 2 = z 3 ⇒ 2 + λ 1 + 1 - 2 λ 2 + 3 λ 3 = 0 ⇒ λ = - 2 3 ⇒ 3 + 4 u 1 + - 1 + 5 u 2 + 1 - 2 u 3 = 0 ⇒ 8 u + 4 = 0 ⇒ u = - 1 2 Equation of bo

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