Answer
The required vector is $(0.707~\hat{i}+0.707~\hat{j})$
Work Step by Step
The vector ($\hat{i}+\hat{j}$) points at a $45^{\circ}$ angle above the positive x-axis. The vectors which point in this direction have the form $(k\hat{i}+k\hat{j})$ for some positive constant $k$. Therefore,
$\sqrt{k^2+k^2} = 1$
$\sqrt{2k^2} = 1$
$k = \frac{1}{\sqrt{2}}$
$k = 0.707$
This means that the required vector is $(0.707~\hat{i}+0.707~\hat{j})$.
