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A plane $π$ 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 $π$ is

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$23 x + 29 y - 29 z = 23$

$31 x + 27 y + 3 z = 71$

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

$29 x + 31 y + 3 z = 63$

answer is C.

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Detailed Solution

$d r' s (b, c, a) = (23, 29, 3)$

$23 (x - 1) + 29 (y - 1) + 3 (z - 1) = 0$

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

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