Question

Find the unit vector in the direction of (-2, -1).Write your answer in component form.Do not approximate any numbers in your answer. ( , )

Answer 1

A unit vector has a module of 1.

We can calculate the coordinates of a unit vector in the direction of an specific vector by dividing the coordinates of that vector by the module.

Then, first we will calculate the module of the vector:

$\begin{gathered} |r|=\sqrt[]{x^2+y^2} \\ |r|=\sqrt[]{(-2)^2+(-1)^2} \\ |r|=\sqrt[]{4+1} \\ |r|=\sqrt[]{5} \end{gathered}$

We then can write the unit vector as:

$r=(-\frac{2}{\sqrt[]{5}},-\frac{1}{\sqrt[]{5}})=(-\frac{2\sqrt[]{5}}{5},-\frac{\sqrt[]{5}}{5})$

Answer: (-2√5/5, -√5/5)