HMMT 2004 U2

If the three points

$\begin{aligned} & (1, a, b) \\ & (a, 2, b) \\ & (a, b, 3) \end{aligned}$

are collinear (in 3 -space), what is the value of $a+b$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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