Answer
$\textbf{0}=(0,0,0,0)$.
Work Step by Step
Since the zero vector, $\textbf 0$, has the property that $$u+\textbf{ 0}=u,$$
then the zero vector of the vector space $R^4$ can be calculated as follows;
Let $\textbf{0}=(a,b,c,d)$ be the zero vector of $R^4$, then for any vectro $(x,y,z,w) \in R^4$, we have
$$(x,y,z,w) +(a,b,c,d)=(x,y,z,w) .$$
By comparing the components in the above equation we find that $\textbf{0}=(a,b,c,d)=(0,0,0,0)$.
