Since, the line is equally inclined to the axes and passes through the origin, its direction ratios are 1,1,1.
So, its equation is
=
=
A point P on it is given by (a, a, a). So, equation of the plane through P (a, a, a) and perpendicular to OP is 1 (x - a) + 1 (y- a) + 1 (z - a) = 0
(Since OP is normal to the plane)
i.e.,x + y+z = 3a
⇒
++ = 1
Intercepts on axes are 3 a, 3 a and 3 a, therefore sum of reciprocals of these intercepts.
=
++ =