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

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

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

Solution:

It is known to us that, eq. of a line passing through $\left(x_{1}, y_{1}, z_{1}\right)$ and parallel to a line with direction ratios $a, b, c$ is
$\frac{\mathrm{x}-\mathrm{x}_{1}}{\mathrm{a}}=\frac{\mathrm{y}-\mathrm{y}_{1}}{\mathrm{~b}}=\frac{\mathrm{Z}-\mathrm{z}_{1}}{\mathrm{c}}$
Given that, the line passes through origin i.e. $(0,0,0)$
$\mathrm{x}_{1}=0, \mathrm{y}_{1}=0, \mathrm{z}_{1}=0$
As line is parallel to $x$ – axis,
$a=1, b=0, c=0$
$\therefore$ Eq. of Line is given by
$\begin{array}{l} \frac{\mathrm{x}-0}{1}=\frac{\mathrm{y}-0}{0}=\frac{\mathrm{Z}-0}{0} \\ \frac{\mathrm{x}}{1}=\frac{\mathrm{y}}{0}=0 \end{array}$