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Formula: Position Vector of a Point Partitioning a Line Segment by a Ratio. Let 𝑃 be a point on line segment 𝐴 𝐵 , partitioning it in the ratio 𝑚 ∶ 𝑛 . Then, the position vector 𝑂 𝑃 is given by 𝑂 𝑃 = 𝑚 𝑚 + 𝑛 𝑂 𝐵 + 𝑛 𝑚 + 𝑛 𝑂 𝐴 .
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