A vector is a list of $N$ numbers and can be thought of as a direction in some $N$-dimensional space. $\huge \begin{align} \let \vec v &\in \Rn n \\ \vec v &= \mat{ v_{1}\\v_{2} \\ \vdots \\v_{n} }\\ &= \ang{ v_{1},v_{2}, \dots, v_{n} } \end{align}$ >[!tip]- Difference between [[Vector|Vectors]] and a [[Point]] ([[Geometry|Geometric Sense]]) >A vector is not a [[Point]] and are used in difference places. > >There is **no** *absolute position*, it only describes *relative movement*. >- Vectors have a set [[Vector Direction|direction]] and *[[Vector Magnitude|magnitude]]*. >- A vector is **not** a difference between any specific points, but can still describe the relationship between different points > - Vector addition is *commutative* The difference of [[Point|Points]] is a [[Vector]] $\huge \begin{align*} P - Q&= \vec{v} \\ P+\vec{v} &= Q \\ \vec{a} + \vec{b} &= \vec{v} \\ \end{align*} $ >[!seealso] See Also: [[Vector Arithmetic]]