MHB Position vector question. Tough to solve.

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The discussion revolves around solving position vector equations involving points P, Q, O, R, and M. The first hint suggests breaking down the vector from P to Q into components from P to O, O to R, and R to Q. The second hint indicates that the vector from O to M can be expressed in terms of the vector from O to P and half the vector from P to Q. Participants are encouraged to complete these vector equations to find the relationships between the points. Completing these equations will clarify the position vectors involved in the problem.
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Hints:

1. $\displaystyle \begin{align*} \vec{PQ} = \vec{PO} + \vec{OR} + \vec{RQ} \end{align*}$. Finish it.

2. $\displaystyle \begin{align*} \vec{OM} = \vec{OP} + \vec{PM} = \vec{OP} + \frac{1}{2}\vec{PQ} \end{align*}$. Finish it.
 

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