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If for $a > 0$, the feet of perpendiculars from the points $A(a, -2a, 3)$ and $B(0, 4, 5)$ on the plane $lx + my + nz = 0$ are points $C(0, -a, -1)$ and $D$ respectively, then the length of line segment $CD$ is equal to:
(1) $\sqrt{31}$
(2) $\sqrt{41}$
(3) $\sqrt{55}$
(4) $\sqrt{66}$
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