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

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

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