Q:

Representing a vector in $\mathbb{R}^{3}$ as sum of only two vectors in $\mathbb{R}^{3}$

Is it possible?
Or more generally can any vector in $\mathbb{R}^{n}$ can be represented as sum of (n-1) or less vectors in $\mathbb{R}^{n}$?
-----EDIT-----
What I basically want to ask is that can only two vectors in R^3 form the basis of R^3?

A:

The answer is no.
In more detail:  If you choose any two vectors in $\mathbb R^3$, the set of all linear combinations that can be built out of those two vectors will be at most a two-dimensional subspace of $\mathbb R^3$.  If you want to get all of $\mathbb R^3$ then you need three linearly independent vectors.

