Answer
$\vec{v}= \frac{\sqrt2}{2}\hat{i}-\frac{\sqrt2}{2}\hat{j}$
Work Step by Step
We know that the unit vector has magnitude 1, and we know that the x and y components are equal. Thus, we must find these components:
$1 = \sqrt{s^2+s^2} \\ 1 = \sqrt2 s \\ s =\frac{\sqrt2}{2}$
Thus, applying the correct signs, we find:
$\vec{v}= \frac{\sqrt2}{2}\hat{i}-\frac{\sqrt2}{2}\hat{j}$
