Find position vector using midpoint of two other vectors

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SUMMARY

The discussion centers on finding the position vector of a midpoint R between two points P and Q, represented by their position vectors p and q. The correct expression for the position vector r of R is established as r = (1/2)(p + q). This formula simplifies the process of determining the midpoint in vector terms, confirming that the midpoint can be easily calculated using basic vector addition and scalar multiplication.

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  • Familiarity with the concept of midpoints in geometry
  • Basic knowledge of scalar multiplication in vector mathematics
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TheFallen018
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Hi, I've got this problem I'm trying to work out. The problem seems simple, but I don't think I have a good way to construct a way to solve it.

This is the problem.

Let P and Q be two points with position vectors p and q and let
R be a point midway between these two. Find an expression for
the position vector r of R in terms of p and q.


So, the midpoint of P and Q should be \[R=\frac{P+Q}{2}\], however I'm not sure how to turn each of these things into position vectors. Any help would be great. Thanks
 
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Find an expression for
the position vector r of R in terms of p and q.

unless I'm missing something, it seems that you're making this more difficult than it really is ...

$\vec{r} = \dfrac{1}{2}(\vec{p}+\vec{q})$
 

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