If the shortest distance between the lines r =(- i +3 k )+λ( i - a j ) and r =(- j +2 k )+μ( i - j + k ) is √(2/3), then the integral value of a is…

If the shortest distance between the lines $\displaystyle \overrightarrow{\mathbf{r}}=(-\hat{i}+3 \hat{k})+\lambda(\hat{i}-\mathbf{a} \hat{j})$ and $\displaystyle \overrightarrow{\mathrm{r}}=(-\hat{j}+2 \hat{k})+\mu(\hat{i}-\hat{j}+\hat{k})$ is $\displaystyle \sqrt{\frac{2}{3}}$, then the integral value of a is equal to \_\_\_\_.