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JEE Main202116 Mar 2021Morning ShiftMathematicsThree Dimensional GeometryActual

Let the position vectors of two points P and Q be 3 i ^ - j ^ + 2 k ^ and i ^ + 2 j ^ - 4 k ^ , respectively. Let R and S be two points such that the direction ratios of lines P R and Q S are 4 , - 1 , 2 and - 2 , 1 , - 2 , respectively. Let lines P R and Q S intersect at T . If the vector T A → is perpendicular to both P R → and Q S → and the length of vector T A → is 5 units, then the modulu

Options

  1. A482
  2. B171
  3. C5
  4. D227

Correct answer

B. 171

Step-by-step solution

P 3 , - 1 , 2 Q 1 , 2 , - 4 P R →   ‖   4 i ^ - j ^ + 2 k ^ Q S →   ‖   - 2 i ^ + j ^ - 2 k ^ Dr's of normal to the plane containing P , T and Q will be proportional to : i ^ j ^ k ^ 4 - 1 2 - 2 1 - 2 = 4 j ^ + 2 k ^ ∴   ℓ 0 = m 4 = n 2 For point, T : P T → = x - 3 4 = y + 1 - 1 = z - 2 2 = λ Q T → = x - 1 - 2 = y - 2 1 = z + 4 - 2 = μ T ≡ 4 λ + 3 , - λ - 1 , 2 λ + 2 Q ≡ 2 μ + 1 , μ + 2 , - 2

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