Flipping binary figures in a string vector without looping in R

Question

I have a vector with equal sized 0/1 elements, dna. And a similar vector with same size, flip. If the flip = 1, I want to flip the corresponding figure in the dna vector. So 0 would change to 1 and 1 would change to 0. And without looping to make it fast. My real dataset has a lot of data. Below is some sample data:

#input
dna  = c('0101010100', '1010101010', '1010101011')
flip = c('0100000001', '0000000000', '1000000000')

#requested answer
dna_flipped  = c('0001010101', '1010101010', '0010101011')
#first element: second and 10th character is flipped
#second element: nothing is changed
#third element: first character is changed

#try loop solution
flip_split = lapply(strsplit(flip, ''), function(x) which(x == '1'))

for (i in 1:length(dna)){
  for(j in seq_along(flip_split[[i]])){
    k = flip_split[[i]][j]
    substring(dna[[i]],k,k) = as.character(abs(1 - as.integer(substring(dna[[i]],k,k)))) 
  }
}

How can this be done without a loop?