What is Collinear vectors?

Example 15.6

$\vec u\,(3, -2)$ and $\vec v\,(-6, 4)$: $\det = 3 \times 4 - (-6) \times (-2) = 12 - 12 = 0$, collinear (indeed $\vec v = -2\vec u$). $\vec u\,(3, -2)$ and $\vec w\,(2, 1)$: $\det = 3 + 4 = 7 \neq 0$, not collinear.