What is the distance between the $x$-axis and the line through $(0, 3, 4)$ parallel to it?

Explanation

1. 01

   Each point $(t, 3, 4)$ of the line is nearest to $(t, 0, 0)$ on the $x$-axis.

2. 02

   The gap is $\sqrt{3^{2} + 4^{2}} = 5$ all along, so the distance is 5.