Recall that the unit vector in the direction of a vector v≠<0,0> is:
[tex]\vec{u}=\frac{v}{||v||}.[/tex]Notice that:
[tex]||<-2,9>||=\sqrt{(-2)^2+9^2}.[/tex]Simplifying the above result we get:
[tex]||<-2,9>||=\sqrt{4+81}=\sqrt{85}.[/tex]Therefore the unite vector in the direction of <-2,9> is:
[tex]\frac{<-2,9>}{\sqrt{85}}=<-\frac{2}{\sqrt{85}},\frac{9}{\sqrt{85}}>.[/tex]Answer:
[tex]\begin{equation*} <-\frac{2}{\sqrt{85}},\frac{9}{\sqrt{85}}> \end{equation*}[/tex]