r - how to alternatively concatenate 3 strings

I have 3 strings:

a<-c("a1","a2","a3")

b<-c("b1","b2","b3")
c<-c("c1","c2","c3")

How can I get the following output:

"a1","b1","c1","a2","b2","c2","a3","b3","c3"

Here is what I tried:

paste(a,b,c,sep='","')

And what I got:

[1] "a1\",\"b1\",\"c1" "a2\",\"b2\",\"c2" "a3\",\"b3\",\"c3"

Is there a way to do it?
Thank you.

Answer

You could also use

c(rbind(a,b,c))

which (rbind) puts the three variables together into a matrix (row-wise), and then (c()) converts them back into a vector, taking advantage of the fact that R stores matrices in column-wise order.

Some of the diversity of the answers to this question stems (I think) from a lack of clarity on the OP's part (don't know whether this is an issue of understanding or communication ...) between combining individual character strings (e.g. paste("a","b") results in a vector of length 1: "a b")) and combining vectors of character strings (c("a","b") results in a vector of length 2: "a" "b")