MHB Find position vector using midpoint of two other vectors

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To find the position vector of point R, which is the midpoint between points P and Q with position vectors p and q, the correct expression is r = (p + q) / 2. The original poster expressed confusion about converting points into position vectors, but the solution simplifies to averaging the two vectors. The discussion emphasizes that the problem is straightforward and can be resolved with basic vector operations. Overall, the midpoint formula effectively provides the desired position vector.
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 ...

$\vec{r} = \dfrac{1}{2}(\vec{p}+\vec{q})$
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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