Answer
$\dfrac{2}{\sqrt 5}i -\dfrac{1}{\sqrt 5}j$
Work Step by Step
Let us consider two vectors $v=pi+qj$ and $w=xi+yj$; then we have the unit vector $u$ in the same direction as $v$ given by: $u=\dfrac{v}{||v||}$
and the magnitude of any vector (let us say $v$) can be determined using the formula
$||v||=\sqrt{p^2+q^2} $
We have: $||v||=\sqrt {(2)^2+(-1)^2}=\sqrt {5}$
Therefore, the unit vector $u$ in the same direction as $v$ is: $u=\dfrac{v}{||v||}=\dfrac{ 2i -j}{\sqrt 5}=\dfrac{2}{\sqrt 5}i -\dfrac{1}{\sqrt 5}j$
