Find the equation of a line parallel to x-axis and passing through the origin.
Solution and Explanation
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 \(\frac{x}{1}\)=\(\frac{y}{0}\)=\(\frac{z}{0}\)
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