Question

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 

Answer 1

Position vector of B 

OB= ¹/₃   2  +  5
                 3     -3

9 + ²/₃ 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