Barycentric coordinates/Point representation/Exercise/Solution

1. We have

   $P+\overrightarrow{PP}=P+0=P.$

2. We have

   $P+\overrightarrow{PP}+\overrightarrow{PQ}-\overrightarrow{PQ}=P+0=P.$

3. We have

   $\begin{array}{cc}P+\overrightarrow{P,P+v}-\overrightarrow{P,Q+v}+\overrightarrow{PQ}& =P+v+\overrightarrow{Q+v,P}+\overrightarrow{PQ}\\ & =P+v+\overrightarrow{Q+v,Q}\\ & =P+v-v\\ & =P.\end{array}$

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