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))

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

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 ,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 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))

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

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 the normal to the ellipse x^2/25+y^2/1=1 is at a distance p from the origin then the maximum value of p is

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/(p^2)=1/(a^2)+1/(b^2) .