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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A normal line with positive direction cosines to the plane P makes equal angles with the coordinate axes. The distance of the point A 1 , 2 , 3 from the line x - 1 1 = y + 2 1 = z - 3 2 measured parallel to the plane P is equal to

Options

  1. A3 units
  2. B13 units
  3. C14 units
  4. D2 5 units

Correct answer

C. 14 units

Step-by-step solution

Direction ratios of the normal to the plane n → = < 1,1 , 1 > Any general point on the given line is λ + 1 , λ - 2,2 λ + 3 From the diagram A B → = λ , λ - 4,2 λ A B → . n → = 0 ⇒ λ + λ - 4 + 2 λ = 0 ⇒ λ = 1 So, coordinates of the point B are 2 , - 1 ,5 Hence, A B = 1 + 9 + 4 = 14 units

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