If the vectors $\overline{a_1}=x\overline{i}-\overline{j}+\overline{k}$ and $\overline{a_2}=\overline{i}+y\overline{j}+z\overline{k}$ are collinear, then a possible unit vector parallel to the vector $x\overline{i}+y\overline{j}+z\overline{k}$is

$\overline{a_1}, \overline{a_2}\text{\hspace{0.17em} are parallel}$
$\begin{array}{l}\Rightarrow \frac{x}{1}=\frac{-1}{y}=\frac{1}{z}=\lambda \\ x=\lambda ,y=-\frac{1}{\lambda },z=\frac{1}{\lambda }\\ \therefore \text{unit vector parallel to }x\overline{i}+y\overline{j}+z\overline{k}is\\ \frac{\lambda \overline{i}-\frac{1}{\lambda }\overline{j}+\frac{1}{\lambda }\overline{k}}{\sqrt{{\lambda }^2+\frac{1}{{\lambda }^2}+{\frac{1}{{\lambda }^2}}^{ }}}\\ Let\lambda =1\text{ then possible unit vector = }\frac{\overline{i}-\overline{j}+\overline{k}}{\sqrt{3}}\end{array}$