Thank you for reporting, we will resolve it shortly
Q.
The mean free path of a molecule of $He$ gas is $\alpha$. Its mean free path along any arbitrary coordinate axis will be
Kinetic Theory
Solution:
Mean free path of a molecule is the resultant of path along three separate axis and they will be equal.
So, $\alpha=\sqrt{\alpha_{x}^{2}+\alpha_{y}^{2}+\alpha_{2}^{2}}$
where $\alpha_{x}=\alpha_{y}^{2} \alpha_{2}=$ (say) $a$
$\alpha=\sqrt{a^{2}+a^{2}+a^{2}}$
or $a=\frac{\alpha}{\sqrt{3}}$