If a · i = a ·( i + j )= a ·( i + j + k )=1, then a is

If $\displaystyle \overrightarrow{\mathrm{a}} \cdot \hat{\mathrm{i}}=\overrightarrow{\mathrm{a}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}})=\overrightarrow{\mathrm{a}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})=1$, then $\displaystyle \overrightarrow{\mathrm{a}}$ is