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conditional - How to create a new variable with values from different variables if another variable equals a set value in R?

I have a complicated question that I will try to simplify by simplifying my dataset. Say I have 5 variables:

df$Id <- c(1:12)
df$Date <- c(NA,NA,a,a,b,NA,NA,b,c,c,b,a)
df$va <- c(1.1, 1.4, 2.5, ...)     #12 randoms values
df$vb <- c(5.9, 2.3, 4.7, ...)     #12 other random values
df$vc <- c(3.0, 3.3, 3.7, ...)     #12 more random values

Then I want to create a new variable that takes the value from va, vb, or vc if the date is equal to a, b, or c. I had tried a nested if-else, which did not work. I also tried:

df$new[df$date=='a' & !is.na(df$date)] <- df$va
df$new[df$date=='b' & !is.na(df$date)] <- df$vb
df$new[df$date=='c' & !is.na(df$date)] <- df$vc

This correctly left NA's in the new variable where Date=NA, however the values provided were not from va, vb, or vc, but some other value altogether. How can I get df$new to equal va if the date is 'a', vb if the date is 'b', and vc if the date is 'c'?

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Try

library(dplyr)
df %>% 
    mutate(new = (Date=="a")*va + (Date=="b")*vb + (Date=="c")*vc)
#   Id Date         va        vb         vc       new
#1   1 <NA> 0.26550866 0.6870228 0.26722067        NA
#2   2 <NA> 0.37212390 0.3841037 0.38611409        NA
#3   3    a 0.57285336 0.7698414 0.01339033 0.5728534
#4   4    a 0.90820779 0.4976992 0.38238796 0.9082078
#5   5    b 0.20168193 0.7176185 0.86969085 0.7176185
#6   6 <NA> 0.89838968 0.9919061 0.34034900        NA
#7   7 <NA> 0.94467527 0.3800352 0.48208012        NA
#8   8    b 0.66079779 0.7774452 0.59956583 0.7774452
#9   9    c 0.62911404 0.9347052 0.49354131 0.4935413
#10 10    c 0.06178627 0.2121425 0.18621760 0.1862176
#11 11    b 0.20597457 0.6516738 0.82737332 0.6516738
#12 12    a 0.17655675 0.1255551 0.66846674 0.1765568

Or,

library(data.table)
setDT(df)[,new:= (Date=="a")*va + (Date=="b")*vb + (Date=="c")*vc,]

Data

set.seed(1)
df <- data.frame(Id = 1:12,
                 Date = c(NA,NA,"a","a","b",NA,NA,"b","c","c","b","a"),
                 va = runif(12),
                 vb = runif(12),
                 vc = runif(12), stringsAsFactors = FALSE)

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