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JEE Main2018MathematicsThree Dimensional GeometryActual

If the angle between the lines x 2 = y 2 = z 1 and 5 - x - 2 = 7 y - 14 P = z - 3 4 is cos - 1 2 3 , then P is equal to

Options

  1. A2 7
  2. B7 2
  3. C- 4 7
  4. D- 7 4

Correct answer

B. 7 2

Step-by-step solution

Given lines are x 2 = y 2 = z 1 and 5 - x - 2 = 7 y - 14 p = z - 3 4 ⇒ x - 5 2 = y - 2 P 7 = z - 3 4 We know that the angle between the lines x - x 1 a 1 = y - y 1 b 1 = z - z 1 c 1 and x - x 2 a 2 = y - y 2 b 2 = z - z 2 c 2 is given by θ = cos - 1 a 1 a 2 + b 1 b 2 + c 1 c 2 a 1 2 + b 1 2 + c 1 2 × a 2 2 + b 2 2 + c 2 2 Given, the angle between both lines is cos - 1 2 3 ⇒ cos - 1 2 3 = cos - 1 2 × 2 + 2 × P 7 + 1 × 4 2 2 + 2 2 + 1 2 × 2 2 + P 7 2 + 4 2 ⇒ 2 3 = 4 + 2

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