Question

Equation of line passing through the points (0, 0, 0) and (2, 1, -3) is

• A. \( \frac{x}{2} = \frac{y}{1} = \frac{z}{-3} \)
• B. \( \frac{x}{2} = \frac{y}{1} = \frac{z}{3} \)
• C. \( \frac{x}{1} = \frac{y}{2} = \frac{z}{3} \)
• D. \( \frac{x}{3} = \frac{y}{1} = \frac{z}{2} \)

Hint:

Direction ratios are differences in coordinates; line equation uses point and direction ratios.

Answer 1

The Correct Option is A

Direction ratios: Difference between points (2, 1, -3) and (0, 0, 0): 
\[ (2-0, 1-0, -3-0) = (2, 1, -3). \] Line equation through origin (0, 0, 0) with direction ratios (2, 1, -3): \[ \frac{x-0}{2} = \frac{y-0}{1} = \frac{z-0}{-3} \Rightarrow \frac{x}{2} = \frac{y}{1} = \frac{z}{-3}. \] Answer: \( \frac{x}{2} = \frac{y}{1} = \frac{z}{-3} \).