You can use the match function of R to find the positions of all elements of a vector in another vector.
The format of the match function is as follows:
match(x, table, nomatch = NA_integer_, incomparables = NULL)
where, x = your small vector, table = your big vector
Here is an example:
bigVec <- c(11:20)
smallVec <- c(12,14,15,16)
The above code will return 2 4 5 6.