Given $\vec{a}=2\hat{i}$, $\vec{b}=\hat{i}+\hat{j}+\hat{k}$, $\vec{c}=2\hat{k}$ and $\vec{x}-\vec{w}=\vec{v}$ where $\vec{w}=\vec{b}-\vec{a}$ and $\vec{v}=\vec{b}-\vec{c}$. Then $\vec{x}$ is:

1. A
   $2\hat{j}$
2. B
   $2\hat{k}$
3. C
   $\hat{j}+\hat{k}$
4. D
   $\hat{j}-\hat{k}$