The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$ is

perpendicular to z-axis

Equations of x, y and z-axis are

$\frac{x}{1}=\frac{y}{0} =\frac{z}{0}, \frac{x}{0}=\frac{y}{1} =\frac{z}{0}$ and $ \frac{x}{0}=\frac{y}{0} =\frac{z}{1}$ respectively.

The given line is $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$

We observe that $3× 0 + 1×0 + 0 × 1 = 0. $

Hence, the line is perpendicular to z-axis.