PCA - separation and variance

I have a multi-dimensional data set containing two different groups of
data I want to separate utilizing PCA. I observed (by eye) that a
certain set of variables gives me a good separation using the first
three PCs.
What is the correlation, if it at all exists, between the separation in
3D to the actual separation in the higher dimensioned plane? How does
the variance of the solution come into play? Can I say that the
separation on the higher dimensioned plane is as good as or perhaps
better/worse than the one in the 3D plane?

.

Relevant Pages

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