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JEE Main202313 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The distance of the point - 1 , 2 , 3 from the plane r → · ( i ^ - 2 j ^ + 3 k ^ ) = 10 parallel to the line of the shortest distance between the lines r → = ( i ^ - j ^ ) + λ ( 2 i ^ + k ^ ) and r → = ( 2 i ^ - j ^ ) + μ ( i ^ - j ^ + k ^ ) is

Options

  1. A4 6
  2. B2 5
  3. C2 6
  4. D3 5

Correct answer

C. 2 6

Step-by-step solution

The direction ratio of line parallel to the line of the shortest distance between the lines r → = ( i ^ - j ^ ) + λ ( 2 i ^ + k ^ ) and r → = ( 2 i ^ - j ^ ) + μ ( i ^ - j ^ + k ^ ) is given by, i ^ j ^ k ^ 2 0 1 1 - 1 1 = i ^ - j ^ - 2 k ^ Now given line passing through A ( – 1 , 2 , 3 ) And having direction ratio ( 1 , – 1 , – 2 ) , So, the equation is given by, x + 1 1 = y - 2 - 1 = z - 3 - 2 = λ Let the line intersect the plane at P P ≡ ( λ - 1 , - λ

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