Subtraction of vectors obeys

Subtraction of vectors does not obey commutative and associative laws but obeys distributive law.

Commutative law:  $\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\ne \overrightarrow{\mathrm{B}}-\overrightarrow{\mathrm{A}}$

Associative law:   $\overrightarrow{\mathrm{A}}-(\overrightarrow{\mathrm{B}}-\overrightarrow{\mathrm{C}})\ne (\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}})-\overrightarrow{\mathrm{C}}$

Distributive law:  $\overrightarrow{\mathrm{A}}·(\overrightarrow{\mathrm{B}}-\overrightarrow{\mathrm{C}})=\overrightarrow{\mathrm{A}}·\overrightarrow{\mathrm{B}}-\overrightarrow{\mathrm{A}}·\overrightarrow{\mathrm{C}}$