Answer
$\dfrac{-2 \sqrt 5}{5}i+\dfrac{\sqrt 5}{5}j$
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 $v$ as:
$u=\dfrac{v}{||v||}$
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: $u=\dfrac{v}{||v||}=\dfrac{ -2i+j}{\sqrt 5}=\dfrac{-2 \sqrt 5}{5}i+\dfrac{\sqrt 5}{5}j$
