Question

\( P \) is a fixed point \( (a, a, a) \) on a line through the origin equally inclined to the axes, then any plane through \( P \) perpendicular to \( OP \), makes intercepts on the axes, the sum of whose reciprocals is equal to

• A. \( \frac{3a}{2} \)
• B. \( \frac{a}{2} \)
• C. \( 2a \)
• D. None of these

Hint:

To find the sum of reciprocals of intercepts, use the properties of planes and geometry.

Answer 1

The Correct Option is A

Step 1: Understanding the geometry.
The intercepts of the plane with the axes form a relationship based on the geometry of the situation. By applying properties of planes and intercepts, we find the sum of the reciprocals equals \( \frac{3a}{2} \).

Step 2: Conclusion.
The sum of the reciprocals is \( \frac{3a}{2} \), corresponding to option (1).