Answer
$\dfrac{1}{\sqrt 2}i -\dfrac{1}{\sqrt 2}j$
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: $||v||=\sqrt {(1)^2+(-1)^2}=\sqrt {2}$
Therefore, the unit vector $u$ in the same direction as $v$ is: $u=\dfrac{v}{||v||}=\dfrac{ -i -j}{\sqrt 2}=\dfrac{1}{\sqrt 2}i -\dfrac{1}{\sqrt 2}j$
