Two systems of rectangular axes have the same origin. If a plane cuts them at distances `a ,b ,ca n da^(prime),b^(prime),c^(prime)` respectively, prove that `1/(a^2)+1/(b^2)+1/(c^2)=1/(a^('2))+1/(b^('2))+1/(c^('2))`

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a ,b ,c and a^(prime),b^(prime),c^(prime) respectively, prove that 1/(a^2)+1/(b^2)+1/(c^2)=1/(a^('2))+1/(b^('2))+1/(c^('2))

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a ,b ,c and a^prime ,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

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

Two system of rectangular axes have the same origin. If a plane cuts them at distance a, b, c and a', b', c' from the origin, then:

If a, b, c are in geometric progression, then prove that : (1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

If a plane has intercepts a, b and c on the coordinate axes and is at a distance of p units from the origin, prove that they (1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))=(1)/(p^(2))

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then 1/(a^2)+1/(b^2)+1/(c^2)=1/(p^2) .

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

Prove that the line x=a y+b ,\ z=c y+d\ a n d\ x=a^(prime)y+b^(prime),\ z=c^(prime)y+d^(prime) are perpendicular if aa^(prime) + c c^(prime) + 1=0