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JEE Main202331 Jan 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Let the plane P : 8 x + α 1 y + α 2 z + 12 = 0 be parallel to the line L : x + 2 2 = y - 3 3 = z + 4 5 . If the intercept of P on the y -axis is 1 , then the distance between P and L is

Options

  1. A2 7
  2. B6 14
  3. C7 2
  4. D14

Correct answer

D. 14

Step-by-step solution

Given, The plane P : 8 x + α 1 y + α 2 z + 12 = 0 be parallel to the line L : x + 2 2 = y - 3 3 = z + 4 5 and the intercept of P on the y -axis is 1 , Now normal of the plane will be perpendicular to the given line, so by perpendicular condition we get, ⇒ 8 × 2 + 3 α 1 + 5 α 2 = 0                     … 1 For Y intercept of plane put x = z = 0 in equation of plane ⇒ y = - 12 α 1 = 1 ⇒ α 1 = - 12 Put α 1

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