Two system of rectangular axes have the same origin. IF a plane cuts them at distances a,b,c and a\',b\',c\'` from the origin then (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`

Options

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`

Answer

c

Explanation

The planes are `(x)/(a)+(y)/(b)+(z)/(c)=1and(x)/(a')+(y)/(b')+(z)/(c')=1`
Since the perpendicular distaance of the origion on the planes is same, therefore,
`|(-1)/(sqrt((1)/a^(2)+(1)/(b^(2))+(1)/(c^(2))))|=|(-1)/(sqrt((1)/(a'^(2))+(1)/(b'^(2))+(1)/(c'^(2))))|`
or `(1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))-(1)/(a'^(2))-(1)/(b'^(2))-(1)/(c'^(2))=0`