Find the equation of a line parallel to x-axis and passing through the origin.

The line parallel to x-­­axis and passing through the origin is x-axis itself.

Let A be a point on x-axis. Therefore, the coordinates of A are given by (a, 0, 0), where a ∈ R.

Direction ratios of OA are (a − 0) = a, 0, 0

The equation of OA is given by,

$\frac{x-0}{a}=\frac{y-0}{0}=\frac{z-0}{0}$

$\Rightarrow \frac{x}{1}=\frac{y}{0}=\frac{z}{0}=a$

Thus, the equation of line parallel to x-axis and passing through origin is

$\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$