question_answer

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b?, c from the origin, then     AIEEE  Solved  Paper-2003

A) \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}+\frac{1}{{{b}^{'2}}}+\frac{1}{c{{'}^{2}}}=0\]

B)  \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}+\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0\]

C)  \[\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}-\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0\]

D)  \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}-\frac{1}{a{{'}^{2}}}-\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0\]

Correct Answer: D

Solution :

Consider OX, OY, OZ and Ox, Oy, Oz are two systems of rectangular axes. Equation of the plane corresponding to OX, OY, OZ as axes is                     Similarly, equation of the plane corresponding to Ox, Oy, Oz as axes is                                       ?. (i) Length of perpendicular from origin to planes (i) and (ii) must be same. i.e.,