Question:
Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and 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
