5. Division of a line segment
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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,
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