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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

Let P 1 , 7 , 2 be a point and the equation of the line L is x - 1 2 = y - 7 1 = z - 2 - 1 . If P Q is the distance of the plane 2 x + y - z = 1 from the point P measured along a line inclined at an angle 60 ° with L , then the length of P Q is

Options

  1. A3 units
  2. B3 2 units
  3. C6 units
  4. D8 units

Correct answer

C. 6 units

Step-by-step solution

Equation of the line through P and parallel to L is x - 1 2 = y - 7 1 = z - 2 - 1 ∵ This line is perpendicular to the plane From the diagram, P R = P Q cos ⁡ 60 ° ⇒ P Q = 2 P R P R = 2 + 7 - 2 - 1 4 = 3 ⇒ P Q = 6 units

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