Given the vector [tex]\vec{u}=(-4,-3).[/tex]
This vector has the length
[tex]|\vec{u}|=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5.[/tex]
Let [tex]\vec{u}_0[/tex] be the unit vector in direction of [tex]\vec{u}.[/tex] If these vectors have the same directions, then they are collinear and, consequently,
[tex]\dfrac{\vec{u}_0}{\vec{u}}=\dfrac{|\vec{u}_0|}{|\vec{u}|},\\ \\\dfrac{\vec{u}_0}{\vec{u}}=\dfrac{1}{5}\Rightarrow \vec{u}_0=\dfrac{\vec{u}}{5}=\left(-\dfrac{3}{5},-\dfrac{4}{5}\right).[/tex]
