Browse Questions

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

$\begin{array}{1 1} \large\frac{x-1}{1}=\large\frac{y}{0}=\large\frac{z}{0} \\ \large\frac{x}{0}=\large\frac{y}{1}=\large\frac{z}{1} \\ \large\frac{x}{1}=\large\frac{y}{0}=\large\frac{z}{0} \\ \large\frac{x}{1}=\large\frac{y}{1}=\large\frac{z}{0} \end{array}$

Toolbox:
• The equation of the lines passing through the points $(x_1,y_1,z_1)$ and direction cosines $l,m,n$ is given by $\large\frac{x-x_1}{l}=\frac{y-y_2}{m}=\frac{z-z_1}{n}$
Step 1:
The line parallel to $x$-axis and passing through the origin is $x$-axis itself.
Let $A$ be the point on $x$-axis.
Therefore the coordinates of $A$ are given by $(a,0,0)$ where $a\in R$
Direction ratios of $OA$ are $(a-0)=(a,0,0)$
Step 2:
The equation of $OA$ is given by
$\large\frac{x-0}{a}=\frac{y-0}{0}=\frac{z-0}{0}$
On simplifying we get
$\Rightarrow \large\frac{x}{a}=\frac{y}{0}=\frac{z}{0}$$=1 (i.e) \large\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$$=a$
Thus the equation of line parallel to $x$-axis and passing through origin is
$\large\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$