We begin by calculating the magnitude of the given vevtor
[tex]|\vec{v}|=\sqrt[]{v^2_1+v^2_2}[/tex]where v₁ and v₂ are the components of the vector. In this case:
[tex]|(-4,5)|=\sqrt[]{(-4)^2+5^2}=\sqrt[]{16+25}=\sqrt[]{41}[/tex]Now, in order to find the unit vector in the direction of a given vector, we calculate
[tex]\frac{\vec{v}}{|\vec{v|}}[/tex]so in this case we have
[tex]\frac{(-4,5)}{\sqrt[]{41}}=(\frac{-4}{\sqrt[]{41}},\frac{5}{\sqrt[]{41}})[/tex]