Claims About Vector Decomposition

Let $\vec a$ be a given nonzero plane vector. Consider the following claims about decomposing $\vec a$ (in each, the vectors $\vec b,\vec c,\vec a$ lie in one plane and are pairwise non-parallel).

1. Given a vector $\vec b$, there always exists a vector $\vec c$ with $\vec a=\vec b+\vec c$. 2. Given vectors $\vec b$ and $\vec c$, there always exist reals $\lambda,\mu$ with $\vec a=\lambda\vec b+\mu\vec c$. 3. Given a unit vector $\vec b$ and a positive number $\mu$, there always exist a unit vector $\vec c$ and a real $\lambda$ with $\vec a=\lambda\vec b+\mu\vec c$. 4. Given positive numbers $\lambda$ and $\mu$, there always exist unit vectors $\vec b$ and $\vec c$ with $\vec a=\lambda\vec b+\mu\vec c$.

Determine, with proof, how many of these claims are true.