The shortest distance between the line passing through the point $\bar{i}+2 \bar{j}+3 \bar{k}$ and parallel to the vector $2 \bar{i}+3 \bar{j}+4 \bar{k}$ and the line passing through the point $2 \bar{i}+4 \bar{j}+5 \bar{k}$ and parallel to the vector $3 \bar{i}+4 \bar{j}+5 \bar{k}$, is