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JEE Main202524 Jan 2025Evening ShiftMathematicsVector AlgebraActual

Let the position vectors of three vertices of a triangle be 4 p + q -3 r ,-5 p + q +2 r and 2 p - q +2 r . If the position vectors of the orthocenter and the circumcenter of the triangle are p + q + r 4 and p + q + r respectively, then +2 +5 is equal to :

Options

  1. A3
  2. B4
  3. C1
  4. D6

Correct answer

A. 3

Step-by-step solution

We know that aligned & O (orthocentre) p + q + r 4 & C ( circum centre) p + q + r & C (centroid) = p + q + r 3 aligned by relation aligned & 2( p + q + r )+ p + q + r 4 =3 ( p + q + r 3 ) & 8( p + q + r )=3( p + q + r ) & 8 =3,8 =3,8 =3 & = 3 8 , = 3 8 , = 3 8 & +2 +3 & 3 8 + 6 8 + 15 8 = 24 8 =3 aligned

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