Two systems of rectangular axes have the same origin

MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a,b,ca, b, c and a′,b′,c′a', b', c' from the origin, then : (1) 1a2+1b2+1c2+1a′2+1b′2+1c′2=0\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 (2) 1a2−1b2−1c2+1a′2−1b′2−1c′2=0\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 (3) 1a2+1b2+1c2−1a′2−1b′2−1c′2=0\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 (4) 1a2−1b2+1c2−1a′2+1b′2−1c′2=0\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

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