Answer
$\frac{i}{\sqrt{2}}-\frac{j}{\sqrt{2}}.$
Work Step by Step
If $v=ai+bj$ then the unit vector $u$ in the direction of $v$ is $u=\frac{v}{||v||}$, where $||v||=\sqrt{a^2+b^2}.$ $||v||=\sqrt{1^2+(-1)^2}=\sqrt{2}.$
Hence $u=\frac{i-j}{\sqrt{2}}=\frac{i}{\sqrt{2}}-\frac{j}{\sqrt{2}}.$