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The points A, B and C lie on a straight line. The position vectors of A and C are 2i + 3j + 9k and 5i - 3j + 4k respectively; B divides AC internally in the ratio 2:1 Find the:

  1. Position vector of B
  2. Distance of B from the Origin 

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Position vector of B 

OB= 1/3   2  +  5
                 3     -3

9 + 2/4
2/3 + 10/3

1       -2
3       -8/3

= 4

= -1
   17/3
 

Distance of B from the Origin 

0B = √42+ (-1)2+ (17/3)2
        _________________
        √ 1b +1+32.11
= √49.11
=7.007 square units

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