What is Collinearity?

Example 6.14

Are $\vec u\,(3, -2)$ and $\vec v\,(-6, 4)$ collinear? Compute $ad - bc = 3 \times 4 - (-2)\times(-6) = 12 - 12 = 0$: yes, and indeed $\vec v = -2\vec u$. For $\vec u\,(3, -2)$ and $\vec w\,(1, 5)$: $3 \times 5 - (-2) \times 1 = 17 \neq 0$: not collinear.