Question

Find the unit vector of n= <-4,-3>

Answer 1

Given:

The vector n is:

`<-4,-3>`

The unit vector is given as:

`\begin{gathered} \text{unit vector=}\frac{vector\text{ n}}{\text{magnitude of vector n}} \\ =\frac{<-4,-3>}{\sqrt[]{(-4)^2+(-3)^2}} \end{gathered}`

Solving further,

`\begin{gathered} \text{unit vector=}\frac{<-4,-3>}{\sqrt[]{16+9}} \\ =\frac{<-4,-3>}{\sqrt[]{25}} \\ =(<-4,-3>)/(5) \end{gathered}`

Thus, the unit vector is given as:

`\begin{gathered} =(1)/(5)<-4,-3> \\ =<(-4)/(5),(-3)/(5)> \end{gathered}`