Unit Vector

Intro

A unit vector is a vector with magnitude 1. To find a unit vector $\hat{u}$ in the same direction of a vector $\vec{v}$, divide $\vec{v}$ by its magnitude $\Vert \vec{v}\Vert$ (length)

$\hat{u}=\frac{\vec{v}}{\Vert \vec{v}\Vert }$

Example: For vector $\vec{v}=(3,4)$:

• Magnitude $=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$.

• Unit Vector $=(\frac{3}{5},\frac{4}{5})$