Notes
vector

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.

Created on June 25, 2021 21:06:16 by Andrew Stacey

Notes vector

Vector

Notes
vector