Semester 1 / Mathematics / Vectors / Section Formula

Section Formula

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Suppose R\text{R} divides the line segment PQ\text{PQ} in the ratio m:nm:n (both are positive and m≥nm \ge n), the division can either be internal or external.

Internally

OR→=mOQ→+nOP→m+n\overrightarrow{\text{OR}} = \frac{m\overrightarrow{\text{OQ}}+n\overrightarrow{\text{OP}}}{m+n}

Externally

External section

OR→=mOQ→−nOP→m−n\overrightarrow{\text{OR}} = \frac{m\overrightarrow{\text{OQ}}-n\overrightarrow{\text{OP}}}{m-n}
Written by September 29, 2026 1 min read
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