The line with direction ratios $1,0,-1$ is inclined with the $z$ -axis at an angle of:

Let the direction ratios be $a=1,b=0,c=-1$.The direction cosine $\cos \gamma$ (where $\gamma$ is the angle with the $z$ -axis) is given by:
$$\cos \gamma =\frac{c}{\sqrt{a^2+b^2+c^2}}$$
$$\cos \gamma =\frac{-1}{\sqrt{1^2+0^2+(-1{)}^2}}=\frac{-1}{\sqrt{2}}$$
$$\gamma ={\cos }^{-1}\left(-\frac{1}{\sqrt{2}}\right)$$
$$\gamma =135^{\circ }=\frac{3\pi }{4}$$