Solution:

Let’s consider the direction cosines of the line be $I, m$ and $n$.
Let $\alpha=90^{\circ}, \beta=135^{\circ}$ and $\mathrm{y}=45^{\circ}$
Therefore,
$I=\cos \alpha, m=\cos \beta \text { and } n=\cos y$
Therefore the direction cosines are
$\begin{array}{l}
I=\cos 90^{\circ}=0 \\
m=\cos 135^{\circ}=\cos \left(180^{\circ}-45^{\circ}\right)=-\cos 45^{\circ}=-1 / \sqrt{2} \\
n=\cos 45^{\circ}=1 / \sqrt{2}
\end{array}$
As a result, the direction cosines of the line are $0,-1 / \sqrt{2}, 1 / \sqrt{2}$