Prove 3 vectors are collinear I am asked to prove A(2,4), B(8,6), C(11,7) are collinear using vectors.

I can work AB by subtracting A from B and BC by subtracting B from C in vector form.

I can say that BC = 2AB.

But I don't understand why this proves they are collinear.
If $A=(2,4), \; B=(8,6), \; C=(11,7)$, then
$$
\vec{AB} = B - A = (6,2) \quad ; \quad
\vec{BC} = C - B = (3,1)
$$
So $\vec{AB} = 2 \vec{BC}$, which is different from your conclusion.

Anyway, this says that $\vec{AB}$ and $\vec{BC}$ are parallel, since one is just a multiple of the other. So, to get from $B$ to $C$, you go in the same direction you went to get from $A$ to $B$ (no turn is required). This means that $A$, $B$, $C$ must all lie on the same line.
Two vectors are colinears (and so your the end points) if, and only if there one is multiple of other.