Two systems of rectangular axes have the same origin. If a plane cuts them at distance `a ,b ,ca n dd ,b^(prime),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`