Line is $\frac{\mathit{x}}{1}=\frac{\mathit{y}}{0}=\frac{\mathit{z}}{0}$ and let point $\mathrm{P}\left(2,5,7\right)$
Direction ratios of line are <1, 0, 0>
This line is x-axis.
Any point on the x-axis has the general co-ordinate (x, 0, 0)
For the x-axis, the foot of perpendicular is simply the x-coordinate of the point P with other co-ordinate being zero.
∴ Foot of perpendicular is Q(2, 0, 0)
∴ Length of the perpendicular is the distance between P(2, 5, 7) & Q(2, 0, 0)
$\therefore \mathit{d}=\sqrt{{\left({\mathit{x}}_2-{\mathit{x}}_1\right)}^2+{\left({\mathit{y}}_2-{\mathit{y}}_1\right)}^2+{\left({\mathit{z}}_2{\mathit{z}}_1\right)}^2}$
$=\sqrt{{\left(2-2\right)}^2+{\left(5-0\right)}^2+{\left(7-0\right)}^2}$
$=\sqrt{0+25+49}$
$=\sqrt{74}$