Prove that if a plane has the intercepts `a ,\ b ,\ c\ a n d\ ` is at a distance of `p` units from theorigin, then `1/(a^2)=1/(b^2)+1/(c^2)=1/(p^2)dot`

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 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))

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

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 ,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))

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)

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 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))

If p be the length of the perpendicular from the origin on the line x//a+y//b =1, then p^2=a^2+b^2 b. p^2=1/(a^2)+1/(b^2) c. 1/(p^2)=1/(a^2)+1/(b^2) d. none of these