weighing proportion of rowSums in dataframe

Dear R-List, 


I am sure there must be a very simple way to do this - I just do not know how...
This is what I want to do: 


#my dataframe

df<-data.frame(id=c("x01","x02","x03","x04","x05","x06"),a=c(1,2,NA,4,5,6),b=c(2,4,6,8,10,NA),c=c(NA,3,9,12,NA,NA),sum=c(3,9,15,24,15,6))

   id    a     b     c   sum
1 x01  1     2    NA   3
2 x02  2     4     3      9
3 x03 NA  6     9     15
4 x04  4     8    12    24
5 x05  5    10   NA  15
6 x06  6   NA  NA   6


#my weights
w<-c(10.5,9,12.8)

#now I want to calculate the proportion of the rowsum = "sum" of every other number in the row, that is df[1,2]/df[1,5], df[1,3]/df[1,5], ...


#e.g. 


df.prop


   id         a         b           c          sum 
1 x01      0.33     0.66     NA        3
2 x02      0.22     0.44     0.33     9
3 x03     NA       0.4       0.6       15
4 x04      0.16     0.33     0.5        24
5 x05      0.33     0.66     NA       15
6 x06      1           NA     NA       6

#and then calculate a rowsum, were each column is weighed by its associated factor in the vector "w", i.e. all entries in column df$a should be weighed by the factor 10.5, df$b by 9 and df$c by 12.8 and then summed up to a weighed rowsum (wrowsum=10.5*0.33+9*0.66).

Any suggestions how to achieve this in a simple way with dataframes that have 9000 rows and 44 columns (so I cannot do this row by row) - sorry, if this is to easy a question.

Thank you very much in advance!

Best wishes

Alain
	[[alternative HTML version deleted]]