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JEE Advanced2020MathematicsThree Dimensional GeometryActual

Let L 1 and L 2 be the following straight lines. L 1 : x − 1 1 = y − 1 = z − 1 3 and L 2 : x − 1 − 3 = y − 1 = z − 1 1 Suppose the straight line L : x − α l = y − 1 m = z − γ − 2 lies in the plane containing L 1 and L 2 , and passes through the point of intersection of L 1 and L 2 . If the line L bisects the acute angle between the lines L 1

Options

  1. Aα − γ = 3
  2. Bl + m = 2
  3. Cα − γ = 1
  4. Dl + m = 0

Correct answer

A. α − γ = 3

Step-by-step solution

Given the lines L 1 : x − 1 1 = y − 1 = z − 1 3 and L 2 : x − 1 - 3 = y − 1 = z − 1 1 . From the given lines, we can say that both the lines pass through the point 1 ,   0 ,   1 . Now, let a → be the direction vector of line L 1 i.e., a → = i - j + 3 k and let b → be the direction vector of line L 2 i.e., b → = - 3 i - j + k . We also know that the angle bisectors lie in the direction of a → + b →   or   a → - b &#8594

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