fill cells in a matrix with one and zeros

I have the next problem:

I have a column with some identificators, for instance:

 id<-c("id1","id2","id3","id4","id5","id6","id7","id8","id9","id10")

then I have have three vectors

 v1<- c("id3","id5","id7")

 v2<- c("id1","id2","id10","id8")

 v3<- c("id5","id9","id10","id3")

I need to create a table, where the first column is the id column (with all the id´s in the three vectors)

Then I need to add three columns in the table and in each column put a 1 if the respective id appears in the vector, and 0 otherwise.

The expected output is something like this

vv1<-c(0,0,1,0,1,0,1,0,0,0)
vv2<-c(1,1,0,0,0,0,0,1,0,1)
vv3<-c(0,0,1,0,1,0,1,0,1,1)

output<-  data.frame(id,vv1,vv2,vv3)

I need this idea in order to replicate the same with a big vector of id’s, around 3M.

Suppose your vectors look like

id <-c("id1","id2","id3","id4","id5","id6","id7","id8","id9","id10")

v1 <- c("id3","id5","id7")
v2 <- c("id1","id2","id10","id8")
v3 <- c("id5","id9","id10","id3")

data.frame(id, 
           vv1 = as.integer(id %in% v1), 
           vv2 = as.integer(id %in% v2), 
           vv3 = as.integer(id %in% v3))

returns

     id vv1 vv2 vv3
1   id1   0   1   0
2   id2   0   1   0
3   id3   1   0   1
4   id4   0   0   0
5   id5   1   0   1
6   id6   0   0   0
7   id7   1   0   0
8   id8   0   1   0
9   id9   0   0   1
10 id10   0   1   1