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JEE Main2017MathematicsThree Dimensional GeometryActual

If the image of the point P 1 , - 2 , 3 in the plane, 2 x + 3 y - 4 z + 22 = 0 measured parallel to the line, x 1 = y 4 = z 5 is Q , then P Q is equal to:

Options

  1. A3 5
  2. B2 42
  3. C42
  4. D6 5

Correct answer

B. 2 42

Step-by-step solution

Any line parallel to x 1 = y 4 = z 5 and passing through P ( 1 , - 2 , 3 ) is    x - 1 1 = y + 2 4 = z - 3 5 = λ    (say) Any point on above line can be written as ( λ + 1 , 4 λ - 2 , 5 λ + 3 ) . ∴ Coordinates of R are ( λ + 1 , 4 λ - 2 , 5 λ + 3 ) . Since, point R lies on the above plane. ∴ 2 ( λ + 1 ) + 3 ( 4 λ - 2 ) - 4 ( 5 λ + 3 ) + 22 = 0 ⇒    λ = 1 So, point R is ( 2 , 2 , 8 ) Now, P R = ( 2 - 1 ) 2 + ( 2 +

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