Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and $a^{1}, b^{1}, c^{1}$ from the origin, then

Moderate

A

$\frac{1}{a^{2}} + \frac{1}{b^{2}} - \frac{1}{c^{2}} + \frac{1}{a^{1^{2}}} - \frac{1}{b^{1^{2}}} - \frac{1}{c^{1^{2}}} = 0$
B

$\frac{1}{a^{2}} - \frac{1}{b^{2}} - \frac{1}{c^{2}} + \frac{1}{a^{1^{2}}} - \frac{1}{b^{1^{2}}} - \frac{1}{c^{1^{2}}} = 0$
C

$\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} - \frac{1}{a^{1^{2}}} - \frac{1}{b^{1^{2}}} - \frac{1}{c^{1^{2}}} = 0$
D

$\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} + \frac{1}{a^{1^{2}}} + \frac{1}{b^{1^{2}}} + \frac{1}{c^{1^{2}}} = 0$

Solution

$\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1, \frac{x}{a^{1}} + \frac{y}{b^{1}} + \frac{z}{c^{1}} = 1$
Distance from (0,0,0)is same

$\frac{1}{\sqrt{\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}}}} = \frac{1}{\sqrt{\frac{1}{{(a^{|})}^{2}} + \frac{1}{{(b^{|})}^{2}} + \frac{1}{{(c^{|})}^{2}}}}$

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