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The prime factors of $2001$ are $3,23\:and\:29$

Equation ofa plane passing through the point $(1,1,1)$ with $d.r.=(b,c,a)$ is given by

$b(x-1)+c(y-1)+a(z-1)=0$

Since it is given that $a,b,c$ are prime factors of $2001$ and

$a<b<c,\:\:a=3,\:b=23\:\:and\:\:c=29$

$\therefore\:$The eqn. of the plane becomes $23x+29y+3z-23-29-3=0$

$i.e.,23x+29y+3z=55$

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