First lets create a vector called Vector1:
set.seed(123)
Vector1 <- rnorm(20)
And add missing data to it:
set.seed(123)
Vector1[sample(1:length(Vector1), 5)] <- NA
Now we can use the is.na function to subset the Vector
Vector1 <- Vector1[!is.na(Vector1)]
Now the resulting vector will have removed the NAs of the original Vector1