:PROPERTIES: :ID: 7898afd8-7728-4375-93a0-07ec5bc43833 :mtime: 20231005013340 :ctime: 20231005013110 :END: #+title: Properties of Vectors #+filetags: :public:project: * Properties of Vectors - Vector addition is commutative: $\textbf{a} + \texbtf{b} = \textbf{b} + \textbf{a}$ - Vector addition is independent of the chosen coordinate system. - additive inverse: $\vec{a} - \vec{a} = \vec{0}$. - Vector addition is associative: $\vec{a} + (\vec{b} + \vec{c}) = (\vec{a} + \vec{b}) + \vec{c}$ - Scalar multiplication distributes over addition: $\lambda (\vec{a} + \vec{b}) = \lambda \vec{a} + \lambda \vec{b}$. - Magnitude distrubes over scalar multiplcation: $| \lambda \vec{a} | = |\lambda||\vec{a}||$.