Plotting vectors in a coordinate system with R or python

An Easy(TM) way to draw a few random magnitude 2 vectors. I first calculate the euclidean norm, else the arrow function will plot arrows from point to point creating a triangle, nice as an explanation, but not what we want. The rest is straightforward:

#first some vectors 
v1<-c(-3,5)
v2<-c(2,-10)
v3 <-c(0,-3)
v4 <- c(2,5)
# This one for the coordinates of the plot
ax<-c(-10,10)
# I will need the euclidean norm (two-norm) of the vectors: 
mag <- function(x) sqrt(sum(x^2))
# I call plot to set up the "canvas"
plot(ax,ax,main="Test")
# I do the stuffz, the FIRST pair of params is the ORIGIN
arrows(0,0, mag(v1),mag(v2),lwd=4,col="red")
arrows(-2,1, mag(v3),mag(v4),lwd=4,col="blue")

Or you can use arrows function in R.

plot(c(0,1),c(0,1))
arrows(0,0,1,1)

plot(NA, xlim=c(0,5), ylim=c(0,5), xlab="X", ylab="Y")
vecs <- data.frame(vname=c("a","b","a+b", "transb"), 
                   x0=c(0,0,0,2),y0=c(0,0,0,1), x1=c(2,1,3,3) ,y1=c(1,2,3,3), 
                   col=1:4)
with( vecs, mapply("arrows", x0, y0, x1,y1,col=col) )

It will look a bit better if you add lwd=3 to the arrows call. The text function would allow labeling and can be rotated with the 'srt' parameter.

plot(NA, xlim=c(0,5), ylim=c(0,5), xlab="X", ylab="Y", lwd=3)
 with( vecs, mapply("arrows", x0, y0, x1,y1,col=col,lwd=3) )
 with(vecs, mapply('text', x=x1[1:3]-.1, y=y1[1:3]+.1, 
  labels=expression(list(a[1],a[2]), list(b[1],b[2]), list(a[1]+b[1],a[2]+b[2]) ) ))

PLease note that the list function inside the expression call is a plotmath list-call, different than the regular R list just as plotmath-paste is different than regular paste. It does not make any attempt to evaluate its argument in the parent-frame. For that one would need bquote or substitute and would probably need to use sapply be used to process the "interior" expressions.