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BITSAT2010MathematicsThree Dimensional GeometryActual

If the middle points of sides ( BC , CA ~ &~ AB ) of triangle (A B C ) 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. A((1 / 3)( i + j + k ) )
  2. B(( i + j + k ) )
  3. C(2( i + j + k ) )
  4. D((2 / 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 2 + 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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