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BITSAT2014MathematicsVector AlgebraActual

If the middle points of sides BC , CA & AB of triangle ABC are respectively D , E , F then position vector of centre of triangle DEF , when position vector of A, B, C are respectively i + j , j + k , k + i is

Options

  1. A1 3 ( i + j + k )
  2. B( i + j + k )
  3. C2( i + j + k )
  4. D2 3 ( i + j + k )

Correct answer

D. 2 3 ( i + j + k )

Step-by-step solution

The position vector of points D, E, F are respectively i + j + k , i + k + j 2 and i + k 2 + j So, position vector of centre of DEF = 1 3 [ i + j 2 + k + i k + j 2 + i + k 2 + j ]= 2 3 [ i + j + k ]

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