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Two systems of rectangular axis have the...

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, then prove that `(1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/((a')^2)+(1)/((b')^2)+(1)/((c')^2)`.

A

`(1)/(a^2)+(1)/(b^2)+(1)/(c^2)+(1)/(a'^2)+(1)/(b'^2)+(1)/(c'^2)=0`

B

`(1)/(a^2)-(1)/(b^2)-(1)/(c^2)-(1)/(a'^2)-(1)/(b'^2)-(1)/(c'^2)=0`

C

`(1)/(a^2)+(1)/(b^2)+(1)/(c^2)-(1)/(a'^2)-(1)/(b'^2)-(1)/(c'^2)=0`

D

`(1)/(a^2)-(1)/(b^2)+(1)/(c^2)-(1)/(a'^2)+(1)/(b'^2)-(1)/(c'^2)=0`

Text Solution

Verified by Experts

The correct Answer is:
(c)
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