# Linear dependence of three vectors

Could someone please explain why, if two vectors in a set of three are parallel to each other, that this implies that the whole set of three vectors is linearly dependent? I have tried to show this algebraically and to understand it graphically but I simply cannot see how one implies the other.

• Consider the (mathematical) condition for two vectors to be parallel. Then compare it to the condition that they are dependent. You'll see ... – Matti P. Apr 17 at 8:07

The vectors would be, say, $$\mathbf v$$, $$k\mathbf v$$ and $$\mathbf w$$. Then $$k\mathbf{v}+(-1)k\mathbf{v}+0\cdot\mathbf{w}=\mathbf{0}$$