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JEE Main20264 April 2026Morning ShiftMathematicsStraight LinesActual

Let the line L₁ : x + 3 = 0 intersect the lines L₂ : x - y = 0 and L₃ : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L₂ and L₃ intersect the line L₁ at the point C . Then BC^2 : AC^2 is equal to:

Options

  1. A5:1
  2. B1:5
  3. C2:3
  4. D3:2

Correct answer

A. 5:1

Step-by-step solution

The intersection point of L₁: x = -3 and L₂: x - y = 0 is A(-3, -3) . The intersection point of L₁: x = -3 and L₃: 3x + y = 0 is B(-3, 9) . The lines L₂ and L₃ intersect at the origin O(0, 0) . The distances from the origin to A and B are: OA = (-3)^2 + (-3)^2 = 3 2 OB = (-3)^2 + 9^2 = 3 10 The angle AOB between the segments OA and OB can be determined using the dot product of vectors OA and OB : OA OB = (-3)(-3) + (-3)(9) = 9 - 27 = -18 Since the dot product is negative, ( AOB) According to the internal angle bise

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