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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

If the foot of perpendicular drawn from the point 2,5 , 1 on a line passing through α , 2 α , 5 is 1 5 , 2 5 , 3 5 , then α is equal to

Options

  1. A19 9
  2. B11 570
  3. C57 54
  4. D1 25

Correct answer

D. 1 25

Step-by-step solution

From diagram P Q → ⋅ Q R → = 0 2 - 1 5 i ^ + 5 - 2 5 j ^ + 1 - 3 5 k ^ · α - 1 5 i ^ + 2 α - 2 5 j ^ + 5 - 3 5 k ^ = 0 ⇒ 9 α 5 - 9 25 + 46 α 5 - 46 25 + 44 25 = 0 ⇒ α = 1 25

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