5. Division of a line segment





We look at a situation similar to the one on the previous page, but allow m and n to have opposite sign. Again, R is the point such that = , and we want to find the position vector of R (relative to O) in terms of the position vectors of P_{1} and P_{2}. Since is a negative multiple of , the vectors and have opposite direction. The point R then lies outside the line segment P_{1}P_{2} (but still on the line joining P_{1} and P_{2}). In these cases, R is said to divide the line segment P_{1}P_{2} externally in the ratio m : n. The formula is, as in case of an internal division,


Feedback 

© 200209 The University of Sydney. Last updated: 09 November 2009
ABN: 15 211 513 464. CRICOS number: 00026A. Phone: +61 2 9351 2222.
Authorised by: Head, School of Mathematics and Statistics.
Contact the University  Disclaimer  Privacy  Accessibility