Question

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

Answer 1

Hint: Assume a point to be on x-axis. The condition given is a line that is parallel to x-axis and passing through origin, if you analyse that line will be x- axis itself. Calculate the coordinates of that point, use this to generate the equation of line.

Complete step-by-step solution -
The line is 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 $\left( {a,0,0} \right),where\,a \in R$
Using the points, we can calculate the direction ratios,
Direction ratios of OA are $\left( {a - 0} \right) = a,0,0.$
The equation of OA is given by,
$\dfrac{{x - 0}}{a} = \dfrac{{y - 0}}{0} = \dfrac{{z - 0}}{0}$
$\dfrac{x}{1} = \dfrac{y}{0} = \dfrac{z}{0} = a$
Thus, the equation of line parallel to x-axis and passing through origin is
$\dfrac{x}{1} = \dfrac{y}{0} = \dfrac{z}{0}$

Note: In these questions, observe the conditions given, as in this one we had to find the equation of a line that was parallel to x-axis and passing through origin, so that clearly means it is the x- axis only.