Formulas of vector operations (addition, subtraction, etc)

Let $\vec{a}$, $\vec{b}$, $\vec{c}$ be vectors and m, n constants.

\[ (\vec{a} + \vec{b}) + \vec{c} = \vec{a} + (\vec{b} + \vec{c}) \\~\\ \vec{a} + \vec{b} = \vec{b} + \vec{a} \\~\\ 1\vec{a} = \vec{a} \\~\\ m\vec{a} + n\vec{a} = (m+n)\vec{a} \\~\\ m\vec{a} + m\vec{b} = m(\vec{a} + \vec{b}) \\~\\ m(n\vec{a}) = (mn)\vec{a} \]

Vector formula

Formula