A plane $\mathrm{\pi }$ passes through the point (1, 1, 1). If b, c, a are the dr’s of a normal to the plane, where a, b, c (a < b < c) are the prime factors of 2001, then the equation of the plane $\mathrm{\pi }$ is

$\begin{array}{l} 2001=3\times 23\times 29\text{ so factors of 2001 are 3,23,29}\\ \Rightarrow \mathrm{a}=3,\mathrm{b}=23,\mathrm{c}=29\\ Now d.r\text{'}s of required plane are (23,29,3) and plane pas\sin g through the point (1,1,1)\\ Required plane is 23(x-1)+29(y-1)+3(z-1)=0\\ \Rightarrow 23x+29y+3z=55\end{array}$