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Two intersecting lines lying in plane P 1 have equations x - 1 1 = y - 3 2 = z - 4 3 and x - 1 2 = y - 3 3 = z - 4 1 . If the equation of plane P 2 is 7 x - 5 y + z - 6 = 0 , then the distance between planes P 1 and P 2 is

Options

  1. A11 5 3
  2. B2 3
  3. C1 3
  4. D7 5 3

Correct answer

B. 2 3

Step-by-step solution

Equation of plane P 1 is x - 1 y - 3 z - 4 1 2 3 2 3 1 = 0 x - 1 - 7 - y - 3 - 5 + z - 4 - 1 = 0 7 x - 5 y + z + 4 = 0 So, distance between planes P 1   &   P 2 is = 10 49 + 25 + 1 = 10 5 3 = 2 3

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