$\overrightarrow {a}. \hat i=\overrightarrow {a}.(2 \hat i +\hat j)= \overrightarrow {a}(\hat i+\hat j+3 \hat k)=1$, then $\overrightarrow a$ is equal to :

Question

\[\begin {array} {1 1} (a)\;\hat i-\hat k & \quad (b)\;1/3(3 \hat i+3 \hat j+\hat k) \\ (c)\;1/3(\hat i+\hat j+\hat k) & \quad (d)\;1/3(3 \hat i-3 \hat j +\hat k)\end {array}\]