The University of Sydney - School of Mathematics and Statistics

External division of a line segment	Page 2 of 2

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 P₁ and P₂.

Since is a negative multiple of , the vectors and have opposite direction.

The point R then lies outside the line segment P₁P₂ (but still on the line joining P₁ and P₂). In these cases, R is said to divide the line segment P₁P₂ externally in the ratio m : n. The formula is, as in case of an internal division,