Question

If \(Q\) is the image of the point \(P(2, 3, 4)\) under the reflection in the plane \(x - 2y + 5z = 6\), then the equation of the line \(PQ\) is

• A. \(\frac{x-2}{1} = \frac{y-3}{-2} = \frac{z-4}{5}\)
• B. \(\frac{x-2}{-1} = \frac{y-3}{2} = \frac{z-4}{-5}\)
• C. \(\frac{x-2}{-1} = \frac{y-3}{-2} = \frac{z-4}{5}\)
• D. \(\frac{x-2}{1} = \frac{y-3}{2} = \frac{z-4}{-5}\)

Hint:

The line joining a point and its reflection in a plane is perpendicular to the plane, hence parallel to the normal vector.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The line \(PQ\) is perpendicular to the plane, so direction ratios are same as normal of plane.

Step 2: Detailed Explanation:
Plane: \(x - 2y + 5z = 6\). Normal vector = \((1, -2, 5)\).
Line through \(P(2, 3, 4)\) with direction \((1, -2, 5)\):
\(\frac{x-2}{1} = \frac{y-3}{-2} = \frac{z-4}{5}\).

Step 3: Final Answer:
Option (A).