# Vector A **vector** describes the relative displacement from one point in the plane to another. It is written in the form $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$ where the first (top) component represents the horizontal displacement (parallel to the $x$-axis) and the second represents the vertical displacement (parallel to the $y$-axis). Positive numbers represent displacement in the positive direction, negative in the opposite. Vectors can be _added_, _subtracted_, and _scaled_ by applying these operations component by component: $$ \begin{aligned} \begin{pmatrix} 3 \\ 4 \end{pmatrix} + \begin{pmatrix} -2 \\ 7 \end{pmatrix} &= \begin{pmatrix} 1 \\ 11 \end{pmatrix} \\ \begin{pmatrix} 3 \\ 4 \end{pmatrix} - \begin{pmatrix} -2 \\ 7 \end{pmatrix} &= \begin{pmatrix} 5 \\ -3 \end{pmatrix} \\ 3\begin{pmatrix} -2 \\ 7 \end{pmatrix} &= \begin{pmatrix} -6 \\ 21 \end{pmatrix} \end{aligned} $$ Two vectors are **parallel** if one is a scale multiple of the other. [[!redirects parallel vector]] [[!redirects parallel vectors]] [[!redirects vectors]]