section formula

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(in vectors)

Let A and B be two points with position vectors a and b, and P a point on the line through A and B, such that AP : PB=m : n. Then P has position vector p, given by the section formula

It is possible to choose m and n such that m+n=1 and thus to suppose, changing notation, that AP : PB=k : 1−k. Then p=(1−k)a+kb.

Subjects: Mathematics.

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