Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' respectively from the origin, then1a2+1b2+1c2=k(1a′2+1b′2+1c′2), where k is equal to

[a] Let a, b, c, be the intercepts when (Ox, Oy, Oz) are taken as exes, then the equation of the plane is xa+yb+zc=1 Let a, b, c be the intercepts when (OX, OY, OZ) are taken as axes; then in this case equation of the same plane is Xa+Xb+Xc=1                               (i) Now, eqs. (i) and (ii) are equation of the same plane and in both the cases the origin is same. Hence, length of the perpendicular drawn from the origin to the plane in both the case must be the same ∴11a2+1b2+1c2−−−−−−−−−−√=11a′2+1b′2+1c′2−−−−−−−−−−−√ ⇒1a2+1b2+1c2=1a′2+1b′2+1c′2 ∴k=1