Practicing Success
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 |
$29 x + 31 y + 3z = 63$ $23 x + 29 y - 29z = 23$ $23 x + 29 y + 3z = 55$ $31 x + 37 y + 3z = 71$ |
$23 x + 29 y + 3z = 55$ |
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. |