# What does it mean to normalize a vector?

It means to divide a vector by its length so that its length becomes 1; for example, the normalized vector $\vec{u}$ of $\vec{v} = \left(3 , 4\right)$ can be found by
$\vec{u} = \frac{\vec{v}}{| \vec{v} |} = \frac{\left(3 , 4\right)}{\sqrt{{3}^{2} + {4}^{2}}} = \frac{\left(3 , 4\right)}{5} = \left(\frac{3}{5} , \frac{4}{5}\right)$.