Question

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

Answer 1

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 $a\in R$.

Direction ratios of $OA$ are $(a-0)=a,0,0$.

The equation of $OA$ is given by,

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

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

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

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