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) .

If a, b, c are in G.P. show that (1)/(a^(2)),(1)/(b^(2)),(1)/(c^(2)) are also in G.P.

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

If p_(1), p_(2) and p_(3) are the altitudes of a triangle from the vertices of a Delta ABC and Delta is the area of triangle, prove that : (1)/(p_(1)) + (1)/(p_(2)) - (1)/(p_(3)) = (2ab)/((a+b+c)Delta) cos^(2).(C )/(2)

If p_(1),p_(2),p_(3) are the altitues of a triangle from the vertieces A,B,C and Delta is the area of the triangle then prove that (1)/(p_(1))+(1)/(p_(2))-(1)/(p_(3))=(2ab)/((a+b+c)Delta)"cos"^(2)(C)/(2)

if P is the length of perpendicular from origin to the line x/a+y/b=1 then prove that 1/(a^2)+1/(b^2)=1/(p^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

If a,b,c are in G.P. and a,x,b,y,c are in A.P., prove that : (1)/(x)+(1)/(y)=(2)/(b)

If p is the perpendicualr distance of the origin from the line whose intercepts on the axes are a and b, show that 1/(p^(2))=1/(a^(2))+1/(b^(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))