Question

A plane $\Pi$ passes through the point $(1,1,1)$. If $b,c,a$ are the direction ratios 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 $\pi$ is

• A. $29x+31y+3z=63$
• B. $23x+29y-29z=23$
• C. $23x+29y+3z=55$
• D. $31x+27y+3z=71$

Answer 1

The correct option is C $23x+29y+3z=55$

Sol. By verification $2001=23\times 29\times 3$

$\therefore 23x+29y+3z=55$