A plane II 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 II is
Answer & explanation
Correct answer: option 3
The equation of the plane is
$b(x-1) + c(y-1) + a(z-1)= 0 $
Now, $2001= 3 × 23 × 29 $
$∴ a < b < c ⇒ a = 3, b = 23 $ and $c = 29$
Substituting the values of a, b, c in (i), we obtain
$23 x + 29 y + 3z = 55$ as the equation of the required plane.