2. If the three points
$$
\begin{array}{l}
(1, a, b) \\
(a, 2, b) \\
(a, b, 3)
\end{array}
$$
are collinear (in 3-space), what is the value of $a+b$ ?
Solution:
4
The first two points are distinct (otherwise we would have $a=1$ and $a=2$ simultaneously), and they both lie on the plane $z=b$, so the whole line is in this plane and $b=3$. Reasoning similarly with the last two points gives $a=1$, so $a+b=4$.