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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} $

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  • 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
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
answered Jun 3, 2013 by sreemathi.v

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