subspace vs space in R

subspace.R

library(rgl)


x <- rep(NA, 20000)
y <- rep(NA, 20000)
z <- rep(NA, 20000)
color <- rep(NA, 20000)

#subspace
for(i in 1:10000){
    a1 = runif(1, -100, 100)
    a2 = runif(1, -100, 100)
    a3 = runif(1, -100, 100)
    x[i] <- a1*3 + a2*-3 + a3*1
    y[i] <- a1*0 + a2*1 + a3*-1
    z[i] <- a1*0 + a2*1 + a3*1
    color[i] <- "black"
} 

#space of all points (orthogonal vectors)
for(i in 10001:20000){
    a1 = runif(1, -500, 500)
    a2 = runif(1, -500, 500)
    a3 = runif(1, -500, 500)
    x[i] <- a1*1 + a2*0 + a3*0
    y[i] <- a1*0 + a2*1 + a3*0
    z[i] <- a1*0 + a2*0 + a3*1
    color[i] <- "blue"
} 

plot3d(x,y,z, col = color)