If the foot of the perpendicular from the origin to a plane is P (a, b, c),the equation of the plane is
xa+yb+zc=3
ax+by+cz=3
ax+by+cz=a2+b2+c2
ax+by+cz=a+b+c
Direction ratios of OP are (a, b, c)Therefore, equation of the plane is
a(x−a)+b(y−b)+c(z−c)=0 i.e., xa+yb+zc=a2+b2+c2