Consider two non-parallel vectors [math]\vec{u}[/math] [color=#1551b5](blue)[/color] and [math]\vec{v}[/math] [color=#c51414](red)[/color] in [math]{\mathbb R}^3[/math]. The vector [math]\vec{w}[/math] [color=#0a971e](green)[/color] is a linear combination of these two vectors. 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 as well as move the whole sketch for a different perspective. Notice that any green vector in the given plane can be written as a linear combination of the other two.