How to multiple the vector and variables from dataframe

hi all:
Here's a dataframe(dat) and a vector(z):
 
dat:
x1     x2    x3
0.2   1.2   2.5
0.5   2      5
0.8   3      6.2
 

z

[1]  10 100 100
 
I wanna do the following:
10*x1,100*x2,1000*x3
 
My solution is using the loop for z and dat(since the length of z is the same as ncol  of dat),which is tedious.
I wanna an efficient solution to do it .

dat=data.frame(x1=1:3, x2=11:13)
dat

as.matrix(dat) * c(3, 2)