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, 0), where a∈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 the origin is \(\frac{x}{1}\)=\(\frac{y}{0}\)=\(\frac{z}{0}\)