It is easy to find simple distance measures for equal-dimension vectors, such as Euclidean Distance or Correlation. What about unequal-dimension vectors, such as, for instance, $(a,b,c)$ and $(d,e)$? Are there any known approaches in math for that?

For example, one approach would be to consider smaller-dimension vectors to be projected: $(a,b,c)$ and $(d,e,0)$. But then I assumed to which plane and potentially I miss $(d,0,e)$. So there is ambiguity. 

Are there any other practically used, especially **non-ambiguous measures**?

Of course generalization to unequal-dimension, even ragged, data arrays is interesting, so please elaborate if you can. 

But some simple computation with $(a,b,c)$ and ($d,e)$ would be very instructive.