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# Two systems of rectangular axis have the same origin.

Question:

Two systems of rectangular axis have the same origin. If a plane cuts them at distances aband a¢, b¢, c¢, respectively, from the origin, prove that

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

Solution:

Let’s take OX, OY, OZ and ox, oy, oz to be two rectangular systems.

And, the equations of two planes are