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AP EAMCET20227 Jul 2022Morning ShiftMathematicsVector AlgebraActual

The vertices of a triangle are at - i +3 j and 2 i +5 j and its orthocenter is at i +2 j . If the position vector of the third vertex is a i +b j , then (a, b)=

Options

  1. A( 5 7 , 5 7 )
  2. B( 5 7 , 17 7 )
  3. C( -5 7 , 17 7 )
  4. D( 5 7 , -17 7 )

Correct answer

B. ( 5 7 , 17 7 )

Step-by-step solution

Let A=(-1,3), B=(2,5), C=(a, b), H=(1,2) . aligned & A E B C & M_ A E M_ B C =-1 aligned ( 3-2 -1-1 ) ( 5-b 2-a )=-1 2 a-b=-1 ...(i) Again m_ A B m_ C D =-1 ( 5-3 2+1 ) ( b-2 a-1 )=-1 3 a+2 b=7 ...(ii) Multiplying of 2 in Eq. (i) and adding Eqs. (i) and (ii) From Eq. (i), b=2 a+1=2 5 7 +1= 17 7 (a, b)= ( 5 7 , 17 7 )

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