You can use this, but there may be a simpler solution :
R> apply(expand.grid(vars, vis), 1, paste, collapse=".")
[1] "SR.1" "PL.1" "SR.2" "PL.2" "SR.3" "PL.3"
expand.grid gives back a data.frame which when used with apply, apply will convert it to a matrix. This is just unnecessary (and inefficient on large data). outer gives a matrix and also takes function argument. It’ll be much efficient on huge data as well.
Using outer:
as.vector(outer(vars, vis, paste, sep="."))
# [1] "SR.1" "PL.1" "SR.2" "PL.2" "SR.3" "PL.3"