I am confused about the coplanarity of vectors, and the relation of coplanarity to linear dependence.
If I have real vectors $\mathbf{u}$, $\mathbf{v}$, and $\mathbf{w}$, with $\mathbf{w}$ a linear combination of $\mathbf{u}$ and $\mathbf{v}$, the three are then linearly dependent. (This much is clear.)
However, I'm not clear on the following:
What does "coplanar" mean? (No, seriously; when I think of three points - vectors - I imagine them as determining a plane a priori; I do not think of two vectors as determining a plane. I imagine that my definition of coplanar is somewhat off here.)
How does linear dependence/independence relate to coplanarity (however it is actually defined)?
Googling (I have Strang's book, which doesn't introduce the notion of linear independence) led me to believe that coplanarity $\iff$ linear dependence (for three vectors), but I do not understand this.
(Also: if you are so inclined, a nice linear algebra reference would be appreciated....)