P→(Q→+R→)=P→⋅Q→+P→⋅R→\overrightarrow{\mathrm{P}}(\overrightarrow{\mathrm{Q}}+\overrightarrow{\mathrm{R}})=\overrightarrow{\mathrm{P}} \cdot \overrightarrow{\mathrm{Q}}+\overrightarrow{\mathrm{P}} \cdot \overrightarrow{\mathrm{R}}P(Q+R)=P⋅Q+P⋅R
P→+Q→=Q→+P→\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}=\overrightarrow{\mathrm{Q}}+\overrightarrow{\mathrm{P}}P+Q=Q+P
(P→+Q→)+R→=P→+(Q→+R→)(\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}})+\overrightarrow{\mathrm{R}}=\overrightarrow{\mathrm{P}}+(\overrightarrow{\mathrm{Q}}+\overrightarrow{\mathrm{R}})(P+Q)+R=P+(Q+R)
P→+Q→=P→⋅Q→\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}=\overrightarrow{\mathrm{P}} \cdot \overrightarrow{\mathrm{Q}}P+Q=P⋅Q