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AP EAMCET202125 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The position vectors of A and B are ( i + j + k ) and . ( 1 3 j + 1 3 k ) ) . If B divides the line A C in the ratio 2: 1 , then position vector C is

Options

  1. A( 1 2 , 0,0 )
  2. B(0, 1 3 , 0 )
  3. C( -1 2 , -1 2 , 0 )
  4. D( -1 2 , 0,0 )

Correct answer

D. ( -1 2 , 0,0 )

Step-by-step solution

Let O A =( i + j + k ) and O B = ( 1 3 j + 1 3 k ) Given ratio = 2 : 1 Let m: n = 2:1 m = 2and n = 1 aligned & O B = m O C +n O A m+n = 2 O C+( i + j + k ) 3 & 3 ( 1 3 j + 1 3 k )=2( OC )+( i + j + k ) & j + k - i - j - k =2 ( OC ) & OC = -1 2 i +0 j +0 k & C= ( -1 2 , 0,0 ) & aligned

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