Question

The line which passes through the origin and intersects the two lines \[ \frac{x - 1}{2} = \frac{y - 3}{4} = \frac{z - 14}{4} \] is

• A. \( \frac{x}{3} = \frac{y}{5} = \frac{z}{5} \)
• B. \( \frac{x}{3} = \frac{y}{5} = \frac{z}{7} \)
• C. \( \frac{x}{3} = \frac{y}{2} = \frac{z}{5} \)
• D. \( \frac{x}{5} = \frac{y}{7} = \frac{z}{5} \)

Hint:

To find the equation of a line passing through the origin, express the direction ratios of the line in the required format.

Answer 1

The Correct Option is C

To find the equation of the line passing through the origin and intersecting the given lines, use the concept of direction ratios and solve the system of equations by cross-multiplying the ratios.
Final Answer: \[ \boxed{\frac{x}{3} = \frac{y}{2} = \frac{z}{5}} \]