Question

Determine the unit vector in the direction of <-2, 9>.

Answer 1

Recall that the unit vector in the direction of a vector v≠<0,0> is:

`\vec{u}=(v)/(||v||).`

Notice that:

`||<-2,9>||=√((-2)^2+9^2).`

Simplifying the above result we get:

`||<-2,9>||=√(4+81)=√(85).`

Therefore the unite vector in the direction of <-2,9> is:

`(<-2,9>)/(√(85))=<-(2)/(√(85)),(9)/(√(85))>.`

Answer:

`\begin{equation*} <-(2)/(√(85)),(9)/(√(85))> \end{equation*}`