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JEE Main201912 Apr 2019Evening ShiftMathematicsThree Dimensional GeometryActual

The length of the perpendicular drawn from the point ( 2 , 1 , 4 ) to the plane containing the lines r → = i ^ + j ^ + λ i ^ + 2 j ^ - k ^ and r → = ( i ^ + j ^ ) + μ ( - i ^ + j ^ - 2 k ^ ) is

Options

  1. A1 3
  2. B3
  3. C3
  4. D1 3

Correct answer

C. 3

Step-by-step solution

n → = i j k 1 2 - 1 - 1 1 - 2 = - 3 i ^ + 3 j ^ + 3 k ^ Equation of plane - 3 x - 1 + 3 y - 1 + 3 z = 0 ⇒ x - y - z = 0 d ( 2,1 , 4 ) = | 2 - 1 - 4 | 1 2 + 1 2 + 1 2 = 3

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