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`

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))

A plane makes intercepts 1,2, 3 on the coordinate axes. If the distance from the origin is p, then the value of p is

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 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

Find the vector equation of the plane passing through the points A(a,0,0),B(0,b,0) and C(0,0,c) . Reduce it to normal form.If plane ABC is at a distance p from the origin,prove that (1)/(p^(2))=(1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))

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))

If a plane makes intercepts 2,2,1 on X-,Y- and Z- axes respectively, then its perpendicular distance from the origin is

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))