What is Collinear vectors? — Mathematics

Definition 15.3 High School Mathematics · Chapter 15 — Vectors and Lines in the Plane

Two vectors are collinear if one is a scalar multiple of the other: $\vec v = \lambda \vec u$ for some $\lambda \in \R$ (or $\vec u = \vec 0$ ). Geometrically: they have the same direction, or one of them is zero.

Examples

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.

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