The shortest distance between the line through $\hat{i}+2\hat{j}+3\hat{k}$ parallel to $2\hat{i}+3\hat{j}+4\hat{k}$ and the line through $2\hat{i}+4\hat{j}+5\hat{k}$ parallel to $3\hat{i}+4\hat{j}+5\hat{k}$ is