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JEE Main202528 Jan 2025Evening ShiftMathematicsVector AlgebraActual

Let A, B, C be three points in x y -plane, whose position vector are given by 3 i + j , i + 3 j and a i +(1- a ) j respectively with respect to the origin O . If the distance of the point C from the line bisecting the angle between the vectors OA and OB is 9 2 , then the sum of all the possible values of a is :

Options

  1. A2
  2. B9 / 2
  3. C1
  4. D0

Correct answer

C. 1

Step-by-step solution

Equation of line in the internal bisector of O A and O B is ( 3 +1) i +( 3 +1) j line will be y=x x-y=0D= | a-(1-a) a^2+(1-a)^2 |= 9 2 aligned & (2 a-1)^2= 81 2 (a^2+(1-a)^2 ) & 2 (4 a^2-4 a+1 )=81 a^2+81 a^2-162 a-81 & 162 a^2-162 a+81-8 a^2+8 a-2=0 & 154 a^2-154 a+79=0 & Sum of values =- (-154) 154 =1 aligned

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