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 distance a ,b ,cand 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 distance 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 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

Two system of rectangular axes have the same origin. If the plane cuts the axes at dostances a, b, c to the first system and a', b', c' to the second system of rectangular axes from the origin then

If a,b, and c are in G.P.then prove that (1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

Prove that , Prove that 1+a^(2),ab,acab,1+b^(2),bcca,cb,1+c^(2)]|=1+a^(2)+b^(2)+c^(2)

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

(1)/(a),a^(2),bc(1)/(b),b^(2),ca(1)/(c),c^(2),ab]|