If the points
\[
(\alpha,4,2),\ (6,\beta,-1)\ \text{and}\ (8,\beta-7)
\]
are collinear, then \(\alpha+\beta=\)
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Three points are collinear if the vectors joining them are proportional:
\[
\boxed{\overrightarrow{AB}=\lambda\,\overrightarrow{BC}.}
\]
Compare the corresponding coordinates to determine the unknowns.