## [[Vector]] Two [[Vector|vectors]] are parallel when they hold the same direction, with the magnitude / length being *negligent*. 2 [[Vector|vectors]] are parallel if they are [[Scalar]] multiples of one another. ## *Notation* ### Parallel *Latex Symbol*: `\parallel` $\huge{\vec{u} \parallel \vec{v}}$ ## Not Parallel *Latex Symbol*: `\nparallel` $\huge{\vec{u} \nparallel \vec{v}}$ # Examples ## Parallel ![[../../00 Excalidraw/Parallel .excalidraw.dark.svg|center]] $\huge \vec{u} \parallel \vec{v}$ ## *Non* Parallel ![[../../00 Excalidraw/Parallel _1.excalidraw.dark.svg]] $\huge \vec{u} \nparallel \vec{v}$ ## 0 Vector $\huge\begin{align*} \vec{0} &= \mat{0\\0\\0} \\ \vec{u} &= \mat{2\\-1\\3} \end{align*} $ Whether these two vectors are parallel *depends on context*, most questions will ask *What is any **nonzero** vector parallel?* However in most contexts where we don't ignore, we say that $\vec{0}$ is parallel to any other vector.