Two non-parallel vectors [math]\vec{u}[/math] [color=#1551b5](blue)[/color] and [math]\vec{v}[/math] [color=#c51414](red)[/color] span a plane in [math]{\mathbb R}^3[/math]. Any vector, such as [math]\vec{w}[/math] [color=#0a971e](green)[/color] on the plane spanned by [math]\vec{u}[/math] and [math]\vec{v}[/math] can be written as a linear combination of them. In the sketch you can move [math]\vec{u}[/math], [math]\vec{v}[/math] and [math]\vec{w}[/math] to see how the relationship between them changes.