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JEE Main20203 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual

The lines r → = i ^ - j ^ + l 2 i ^ + k ^ and r → = 2 i ^ - j ^ + m i ^ + j ^ - k ^

Options

  1. ADo not intersect for any values of l and m
  2. BIntersect for all values of l and m
  3. CIntersect when l = 2 and m = 1 2
  4. DIntersect when l = 1 and m = 2

Correct answer

A. Do not intersect for any values of l and m

Step-by-step solution

Lines r → = i ^ - j ^ + l 2 i ^ + k ^ and r → = 2 i ^ - j ^ + m i ^ + j ^ - k ^ Clearly both lines do not have same direction means lines are not parallel. ⇒ Lines are skew lines or intersecting lines. Let lines are skew lines and distance between lines is d if distance between them comes out zero then they will be intersecting lines. For lines r → = a → + λ p → ,   r → = b → + λ q → d = b → - a → · p → × q → p &#

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