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# The equation of the plane passing through the point $(1,1,1)$ and having direction ratios $b,c,a$ $(a < b < c)$, where $a,b,c$ are prime factors of $2001$ is ?

$(a)\:29x+31y+3z=63\:\:\qquad\:(b)\:23x+29y-29x=23\:\:\qquad\:(c)\:23x+29y+3z=55\:\:\qquad\:(d)\:31x+3zy+3z=71$

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 $23x+29y+3z-23-29-3=0$
$i.e.,23x+29y+3z=55$