Answer
a) $W$ is a subspace of $R^3$.
b) $W$ is not a subspace of $R^3$.
Work Step by Step
a) One can see easily that $W$ contains $(0,0,0)$ and closed under addition and closed under scalar multiplication. Hence, $W$ is a subspace of $R^3$.
b) One can see easily that $W$ does not contain $(0,0,0)$ . Hence, $W$ is a subspace of $R^3$.