:PROPERTIES: :ID: 5864974d-0edf-4757-9b1f-31b159c9aa7a :mtime: 20231005011901 :ctime: 20231005011817 :END: #+title: Vectors #+filetags: :public:project: * Physicist's Definition A Physicist would define a vector as something having magnitude and direction. Note that the magnitude is a [[id:2ad0e2ef-f837-43bd-9031-740156b7965a][Scalar]]. * Examples of Vectors ** Position Vector You can define a position vector relative to a given origin. * Euclidean Space For the purposes of convenience, we will mostly be working in Euclidean space. This means that two distinct points uniquely determine a line, and that parallel lines never meet. In Euclidean space, we can use Cartesian Coordinates, which makes life easier. * Notation For the purposes of notation, we will denote vectors with bold script. For example $\textbf{u}$. * Properties of Vectors See [[id:7898afd8-7728-4375-93a0-07ec5bc43833][Properties of Vectors]] * Common Mistakes - Vectors do NOT have a position - $\vec{a}-\vec{a} = \vec{0}$, $\vec{a} - \vec{a} \neq 0$.